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A bibliography on the Secretary Problem in bibtex / bibtopic format (by nature incomplete)
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| % Bibliography on the Secretary Problem and Related Games (Dynkin's game, Poisson search games, etc.) | |
| @Article{Abdelaziz:Krichen:2005, | |
| author = {Ben Abdelaziz, F. and Krichen, S.}, | |
| title = {An Interactive Method for the Optimal Selection Problem with Two Decision Makers}, | |
| journal = {European Journal of Operational Research}, | |
| volume = {162}, | |
| number = {3}, | |
| year = {2005}, | |
| month = {May}, | |
| pages = {602-609}, | |
| abstract = {We develop in this paper an interactive approach for the bilateral optimal selection problem. The decision model involves two decision makers (DMs) observing a sequence of n offers, sequentially, one at a time, in order to choose a compromise offer. Our method is based on an aggregation of the individual expected utilities of the two DMs whenever a conflict occurs. A conflicting situation arises when the two DMs do not agree to choose the same decision. We develop and simulate our approach on different forms of utilities.} | |
| } | |
| @Article{Abdelaziz:Krichen:2007, | |
| author = {Ben Abdelaziz, F. and Krichen, S.}, | |
| title = {Optimal Stopping Problems by Two or More Decision Makers: a Survey}, | |
| journal = {CMS}, | |
| volume = {4}, | |
| number = {}, | |
| year = {2007}, | |
| month = {}, | |
| pages = {89-111}, | |
| abstract = {A review of the optimal stopping problem with more than a single decision maker (DM) is presented in this paper. We classify the existing litera- ture according to the arrival of the offers, the utility of the DMs, the length of the sequence of offers, the nature of the game and the number of offers to be selected. We enumerate various definitions for this problem and describe some dynamic approaches.} | |
| } | |
| @Article{Albright:Derman:1972, | |
| author = {Albright, S. Christian and Derman, Cyrus}, | |
| title = {Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem}, | |
| journal = {Management Science}, | |
| volume = {19}, | |
| number = {1}, | |
| year = {1974}, | |
| month = {September}, | |
| pages = {6 pages} | |
| } | |
| @Article{Albright:1974, | |
| author = {Albright, S. Christian}, | |
| title = {Optimal Sequential Assignments with Random Arrival Times}, | |
| journal = {Management Science}, | |
| volume = {21}, | |
| number = {1}, | |
| year = {1974}, | |
| month = {September}, | |
| pages = {8 pages}, | |
| abstract = {A problem is considered where jobs arrive at random times and assume random values, or importance.} | |
| } | |
| @Article{Albright:1977, | |
| author = {Albright, S. Christian}, | |
| title = {A Bayesian Approach to a Generalized House Selling Problem}, | |
| journal = {Management Science}, | |
| volume = {24}, | |
| number = {4}, | |
| year = {1977}, | |
| month = {December}, | |
| pages = {432-440}, | |
| abstract = {The problem of choosing the one best or several best of a set of sequentially observed random variables has been treated by many authors. For example, the seller of a house has this problem when deciding which bids on the house to accept and which to reject. We assume that the bids are identically distributed random variables and at most n can be observed. Each bid is accepted or rejected when received; a bid rejected now cannot be accepted later on. The object is to maximize the expected value of the bid actually accepted. Unlike most previous authors, we examine the case where one or more parameters of the common underlying distribution are unknown and information on these is updated in a Bayesian manner as the successive random variables are observed. Using the properties of location and scale parameters, an explicit form for the optimal policy is found when the underlying distribution is normal, uniform, or gamma and the prior is from the natural conjugate family. Simulation results concerning sensitivity of the value obtained to the amount and correctness of the prior information for these three families is then presented.} | |
| } | |
| @Article{Ali:1998, | |
| author = {Ali, Mukhtar M.}, | |
| title = {Probability Models on Horse-Race Outcomes}, | |
| journal = {Journal of Applied Statistics}, | |
| volume = {25}, | |
| number = {2}, | |
| year = {1998}, | |
| month = {}, | |
| pages = {221-229}, | |
| abstract = {A number of models have been examined for modelling probability based on rankings. Most prominent among these are the gamma and normal probability models. The accuracy of these models in predicting the outcomes of horse races is investigated in this paper. The parameters of these models are estimated by the maximum likelihood method, using the information on win pool fractions. These models are used to estimate the probabilities that race entrants finish second or third in a race. These probabilities are then compared with the corresponding objective probabilities estimated from actual race outcomes. The data are obtained from over 15 000 races. it is found that all the models tend to overestimate the probability of a horse finishing second or third when the horse has a high probability of such a result, but underestimate the probability of a horse finishing second or third when this probability is low.} | |
| } | |
| @Article{Alpern:Gal:Solan:1998, | |
| author = {Alpern, Steve and Gal, Shmuel and Solan, Eilon}, | |
| title = {A Sequential Selection Game with Vetoes}, | |
| journal = {Games and Economic Behavior}, | |
| volume = {68}, | |
| number = {}, | |
| year = {1998}, | |
| pages = {1-14}, | |
| abstract = {We study a selection game between two committee members (the players). They interview candidates sequentially and have to decide, after each interview, whether to hire the candidate or to interview the next candidate. Each player can either accept or reject the candidate, and if he rejects the candidate while the other accepts her, he can cast a veto. The candidate is hired if accepted by at least one player and not vetoed. The total number of vetoes available for each player are fixed in advance. We prove the existence of a subgame perfect equilibrium if there are a finite number of candidates types. For a general candidate distribution we prove the existence of a subgame perfect $\epsilon$-equilibrium. We exhibit situations in which a player prefers that the other player would have an extra veto, and even prefers to give one of his vetoes to the other player.} | |
| } | |
| @Article{Alpern:Gal:2009, | |
| author = {Alpern, Steve and Gal, Shmuel}, | |
| title = {Analysis and Design of Selection Committees: A Game Theoretic Secretary Problem}, | |
| journal = {International Journal of Game Theory}, | |
| volume = {38}, | |
| number = {}, | |
| year = {2009}, | |
| month = {}, | |
| pages = {377-394}, | |
| abstract = {Firms often delegate important decisions to committees which are set up specifically for that purpose; for example selection committees. We analyze the equilibrium behavior of a game in which committee members (the players) interview candidates sequentially, either hiring or going on to the next one. The players have differing evaluations of candidates (e.g. one cares about typing skills; the other about IT skills), which become their utilities if the candidate is hired. We then consider the optimal design (rules of the game) of such a committee, from the point of view of the firm. That is, which rules hire candidates which maximize the firm’s utility. Our committee game has a first round in which the members sequentially, by order of player number, say `yea' or `nea' to the candidate. If there are sufficient `yeas' then she is tentatively hired; otherwise she is rejected. In the former case, members who said nea can veto the candidate in the second round. Thus the candidate is either hired, rejected, or vetoed. In the last case, the member casting a veto has one less to use on later candidates. We analyze equilibria where a player may say `yea' to a candidate he would prefer not to hire, in order to force the other player to use up a valuable veto. We show that for the uniform candidate distribution there is a unique equilibrium and better candidates for the firm are hired when there are more vetoes.} | |
| } | |
| @Article{Ano:1989, | |
| author = {Ano, Katsunori}, | |
| title = {Optimal Selection Problem with Three Stops}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {32}, | |
| number = {4}, | |
| year = {1989}, | |
| pages = {491--504}, | |
| abstract = {Optimal selection problem with multiple choices, like secretary, dowry or marriage problems have attracted attention of many applied mathematicians and are also of great significance for those who are looking for ``the best partner''. In this paper we consider a variation of the optimal selection problem with three stops allowed which is often referred to as the secretary problem with multiple choices where the objective is to find an optimal stopping rule so as to maximize the probability of selecting three absolute bests. We also present a set of dynamic programming equations for the problems both of selecting the best object with three stops and of selecting two absolute bests with three stops. For those problems the optimal stopping rules are numerically calculated in aid of computer programming.} | |
| } | |
| @Article{Ano:1990, | |
| author = {Ano, Katsunori}, | |
| title = {Bilateral Secretary Problem Recognizing the Maximum or the Second Maximum of a Sequence}, | |
| journal = {Journal of Information and Optimization Sciences}, | |
| volume = {11}, | |
| number = {1}, | |
| year = {1990}, | |
| pages = {177-188}, | |
| abstract = {We consider a bilateral secretary problem of which model is as follows: n objects appear sequentially and completely randomly for the players I, II. The player I has the first option to stop and accept this object or to reject it, if and only if the player I rejects it then the player II has the same option. Knowledge about the current object (jth) is restricted to its relative rank among the first j objects which has already appeared and both players the same knowledge at any point. We call “win” for the player to stop and accept the best object (absolute rank 1 of all) or the second best object (absolute rank 2 of all). If this event ``win'' attains by some player, he gain a payoff of which structure is defined in section 1. When one player stops, the other player cannot stop and only observes. This game is formulated by zero sum game without recall. We derive the optimal stopping policies for both players and the value of the game. Moreover we study the asymptotic case.} | |
| } | |
| @Article{Ano:1992, | |
| author = {Ano, Katsunori}, | |
| title = {A Secretary Problem With Restricted Offering Chances and Random Number of Applications}, | |
| journal = {Computers and Mathematics with Applications}, | |
| volume = {24}, | |
| number = {1/2}, | |
| year = {1992}, | |
| pages = {157--162}, | |
| abstract = {This article considers a modification of the secretary problem with random number of applicants discussed by Presman and Sonin [1]. Our problem also allows both uncertainty of employment and restriction of offering chances, that is, an offer of acceptance is declined by the applicant with a fixed known probability $1-p$, ($0 \leq p \leq 1$) and the offering chances, before the decision maker gets one applicant, are at most $M$ times. Section 2 gives the sufficient condition for the problem to be monotone and the optimal strategy of the monotone problem. In Section 3 we give the examples for uniform distribution of random number of applicants.} | |
| } | |
| @Article{Ano:2001, | |
| author = {Ano, Katsunori}, | |
| title = {Multiple Selection Problem and OLA Stopping Rule}, | |
| journal = {Scientiae Mathematicae Japonicae}, | |
| volume = {4}, | |
| year = {2001}, | |
| pages = {469--480} | |
| } | |
| @Incollection{Ano:Ando:2000, | |
| author = {Ano, Katsunori and Ando, Masakazu}, | |
| title = {A Note on Bruss' Stopping Problem With Random Availability}, | |
| booktitle = {Game Theory, Optimal Stopping, Probability and Statistics}, | |
| editor = {Bruss, F. Thomas and Le Cam, Lucien}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Lecture Notes--Monograph Series}, | |
| volume = {35}, | |
| year = {2000}, | |
| pages = {71--82} | |
| } | |
| @Techreport{Ano:Kakinuma:Miyoshi:2010, | |
| author = {Ano, Katsunori and Kakinuma, Hideo and Miyoshi, Naoto}, | |
| title = {Odds Theorem with Multiple Selection Chances}, | |
| journal = {Published in: Applied Probability Trust}, | |
| type = {Research Reports on Mathematical and Computing Science}, | |
| institution = {Department of Mathematical and Computing Sciences, Tokyo Institute of Technology}, | |
| number = {B-461}, | |
| year = {2010}, | |
| month = {March}, | |
| pages = {1-10}, | |
| abstract = {We study the multi-selection version of so-called odds theorem by Bruss (2000). We observe a finite number of independent $0/1$ (failure/success) random variables sequentially and want to select the last success. We derive the optimal selection rule when we are given $m$ ($\geq 1$) selection chances and find that the optimal rule has the form of combination of multiple odds-sums. We provide a formula for computing the maximum probability of selecting the last success when we have m selection chances and also give closed-form formulas for $m = 2$ and $3$. For $m = 2$, we further give the bounds for the maximum probability of selecting the last success and derive its limit as the number of observations goes to infinity. An interesting implication of our result is that the limit of the maximum probability of selecting the last success for $m = 2$ is consistent to the corresponding limit for the classical secretary problem with two selection chances.} | |
| } | |
| @Techreport{Ano:Tamaki:1992, | |
| author = {Ano, Katsunori and Tamaki, Mitsushi}, | |
| title = {A Secretary Problem with Uncertain Employment and Restricted Offering Chances}, | |
| type = {Center for Management Studies Working Paper Series}, | |
| institution = {Nanzan University}, | |
| number = {9105}, | |
| year = {1992} | |
| } | |
| @Article{Ano:Tamaki:Hu:1996, | |
| author = {Ano, Katsunori and Tamaki, Mitsushi and Hu, MuCi}, | |
| title = {A Secretary Problem with Uncertain Employment When the Number of Offers is Restricted}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {39}, | |
| number = {3}, | |
| year = {1996}, | |
| pages = {307--315} | |
| } | |
| @Article{Arrow:Blackwell:Girshick:1949, | |
| author = {Arrow, Kenneth J. and Blackwell, David and Girshick M. A.}, | |
| title = {Bayes and Minimax Solutions of Sequential Decision Problems}, | |
| journal = {Econometrica}, | |
| volume = {17}, | |
| number = {3/4}, | |
| year = {1949}, | |
| month = {July-October}, | |
| pages = {213-244}, | |
| abstract = {The present paper deals with the general problem of sequential choice among several actions, where at each stage the options available are to stop and take a definite action or to continue sampling for more information. There are costs attached to taking inappropriate action and to sampling. A characterization of the optimum solution is obtained first under very general assumptions as to the distribution of the successive observations and the costs of sampling; then more detailed results are given for the case where the alternative actions are finite in number, the observations are drawn under conditions of random sampling, and the cost depends only on the number of observations. Explicit solutions are given for the case of two actions, random sampling, and linear cost functions.} | |
| } | |
| @Article{Assaf:Goldstein:SamuelCahn:1998, | |
| author = {Assaf, David and Goldstein, Larry and Samuel-Cahn, Ester}, | |
| title = {A Statistical Version of Prophet Inequalities}, | |
| journal = {The Annals of Statistics}, | |
| volume = {26}, | |
| number = {3}, | |
| year = {1998}, | |
| month = {June}, | |
| pages = {1190--1197} | |
| } | |
| @Techreport{Assaf:Goldstein:Samuel-Cahn:2003, | |
| author = {Assaf, David and Goldstein, Larry and Samuel-Cahn, Ester}, | |
| title = {Odds Theorem with Multiple Selection Chances}, | |
| type = {Discussion Paper of the Center for the Study of Rationality}, | |
| institution = {The Hebrew University of Jerusalem}, | |
| number = {306}, | |
| year = {2003}, | |
| month = {January}, | |
| pages = {1-31} | |
| } | |
| @Article{Assaf:Goldstein:SamuelCahn:2002, | |
| author = {Assaf, David and Goldstein, Larry and Samuel-Cahn, Ester}, | |
| title = {Ratio Prophet Inequalities When the Mortal has Several Choices}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {12}, | |
| number = {3}, | |
| year = {2002}, | |
| month = {August}, | |
| pages = {972--984} | |
| } | |
| @Article{Assaf:SamuelCahn:2002, | |
| author = {Assaf, David and Samuel-Cahn, Ester}, | |
| title = {Prophet Inequalities for Optimal Stopping Rules with Probabilistic Recall}, | |
| journal = {{B}ernoulli}, | |
| volume = {8}, | |
| number = {1}, | |
| year = {2002}, | |
| month = {February}, | |
| pages = {39--52} | |
| } | |
| @Article{Baharian:Jacobson:2013, | |
| author = {Baharian, Golshid and Jacobson, Sheldon H.}, | |
| title = {Submodular Secretary Problem and Extension}, | |
| journal = {ACM Transactions on Algorithms}, | |
| volume = {27}, | |
| year = {2013}, | |
| pages = {277--296}, | |
| abstract = {The stochastic sequential assignment problem (SSAP) allocates distinct workers to sequentially arriving tasks with stochastic parameters to maximize the expected total reward. In this paper, the assignment of tasks is performed under the threshold criterion, which seeks a policy that minimizes the probability of the total reward failing to achieve a target value. A Markov-decision-process approach is employed to model the problem, and sufficient con-ditions for the existence of a deterministic Markov optimal policy are derived, along with fundamental properties of the optimal value function. An algorithm to approximate the optimal value function is presented, and convergence results are established.} | |
| } | |
| @Article{Bai:1989, | |
| author = {Bai, Z. D.}, | |
| title = {A Theorem of {F}eller Revisited}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {17}, | |
| number = {1}, | |
| year = {1989}, | |
| month = {January}, | |
| pages = {385--395} | |
| } | |
| @Article{Bajnok:Semov:2014, | |
| author = {Bajnok, Bela and Semov, Svetoslav}, | |
| title = {The ``Thirty-Seven Percent Rule'' and the Secretary Problem with Relative Ranks}, | |
| journal = {Discussiones Mathematicae Probability and Statistics}, | |
| volume = {34}, | |
| year = {2014}, | |
| pages = {5--21}, | |
| abstract = {We revisit the problem of selecting an item from n choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first k items and then select the first subsequent item that ranks lower than the l-th lowest-ranked item among the first k. We prove that the optimal rule has k ∼ n/e, as in the classical secretary problem where our sole objective is to select the item of lowest rank; however, with the optimally chosen l, here we can get the expected rank of the item selected to be less than any positive power of n (as n approaches infinity). We also introduce a common generalization where our goal is to minimize the expected rank of the item selected, but this rank must be within the lowest d.} | |
| } | |
| @Article{Bartoszynski:Pleszczynska:1980, | |
| author = {Bartoszynski, R. and Pleszczynska, Z.}, | |
| title = {A Note On the Secretary Problem}, | |
| journal = {Mathematical Statistics {B}anach Center Publications}, | |
| publisher = {{PWN} - {P}olish Scientific Publishers, Warsaw} | |
| volume = {6}, | |
| year = {1980}, | |
| pages = {23--28}, | |
| abstract = {In this note we shall consider a version of the so-called secretary problem when the objective is to find one of the best three candidates.} | |
| } | |
| @Article{Bateni:Hajiaghayi:Zadimoghaddam:2013, | |
| author = {Bateni, Mohammad Hossein and Hajiaghayi, Mohammad Haghi and Zadimoghaddam, Morteza}, | |
| title = {Submodular Secretary Problem and Extension}, | |
| journal = {ACM Transactions on Algorithms}, | |
| volume = {9}, | |
| number = {4}, | |
| year = {2013}, | |
| month = {September}, | |
| pages = {1--23}, | |
| abstract = {Online auction is the essence of many modern markets, particularly networked markets, in which information about goods, agents, and outcomes is revealed over a period of time, and the agents must make irrevocable decisions without knowing future information. Optimal stopping theory, especially the classic secretary problem, is a powerful tool for analyzing such online scenarios which generally require optimizing an objective function over the input. The secretary problem and its generalization the multiple-choice secretary problem were under a thorough study in the literature. In this article, we consider a very general setting of the latter problem called the submodular secretary problem, in which the goal is to select $k$ secretaries so as to maximize the expectation of a (not necessarily monotone) submodular function which defines efficiency of the selected secretarial group based on their overlapping skills. We present the first constant-competitive algorithm for this case. In a more general setting in which selected secretaries should form an independent (feasible) set in each of $l$ given matroids as well, we obtain an $O(l\log^2 r)$-competitive algorithm generalizing several previous results, where $r$ is the maximum rank of the matroids. Another generalization is to consider $l$ knapsack constraints (i.e., a knapsack constraint assigns a nonnegative cost to each secretary, and requires that the total cost of all the secretaries employed be no more than a budget value) instead of the matroid constraints, for which we present a $O(l)$-competitive algorithm. In a sharp contrast, we show for a more general setting of subadditive secretary problem, there is no $\tilde{o}(\sqrt{n})$-competitive algorithm and thus submodular functions are the most general functions to consider for constant-competitiveness in our setting. We complement this result by giving a matching $O(\sqrt{n})$-competitive algorithm for the subadditive case. At the end, we consider some special cases of our general setting as well.} | |
| } | |
| @Article{Bearden:2006, | |
| author = {Bearden, J. Neil}, | |
| title = {A New Secretary Problem with Rank-Based Selection and Cardinal Payoffs}, | |
| journal = {Journal of Mathematical Psychology}, | |
| volume = {50}, | |
| year = {2006}, | |
| pages = {58--59}, | |
| abstract = {We present an extension of the secretary problem in which the decision maker (DM) sequentially observes up to n applicants whose values are random variables $X_1$, $X_2$, ... $X_n$ drawn i.i.d. from a uniform distribution on $[0,1]$. The DM must select exactly one applicant, cannot recall released applicants, and receives a payoff of $x_t$, the realization of $X_t$, for selecting the tth applicant. For each encountered applicant, the DM only learns whether the applicant is the best so far. We prove that the optimal policy dictates skipping the first $\sqrt{n}-1$ applicants, and then selecting the next encountered applicant whose value is a maximum.} | |
| } | |
| @Article{Bearden:Connolly:2007, | |
| author = {Bearden, J. Neil and Connolly, Terry}, | |
| title = {Multi-Attribute Sequential Search}, | |
| journal = {Organizational Behavior and Human Decision Processes}, | |
| publisher = {Elsevier Inc}, | |
| volume = {103}, | |
| year = {2007}, | |
| pages = {147--158}, | |
| abstract = {This article describes empirical and theoretical results from two multi-attribute sequential search tasks. In both tasks, the DM sequentially encounters options described by two attributes and must pay to learn the values of the attributes. In the continuous version of the task the DM learns the precise numerical value of an attribute when she pays to view it. In the threshold version the DM learns only whether the value of an attribute is above or below a threshold that she sets herself. Results from the continuous condition reveal that DMs tended to terminate their searches too early relative to the optimal policy. The pattern reversed in the threshold condition: DMs searched for too long. Maximum likelihood comparisons of two different stochastic decision models showed that DMs under both information conditions performed in ways consistent with the optimal policies. Those offered continuous-valued attribute information did not, however, spontaneously degrade this information into binary (acceptable/unacceptable) form, despite the theoretical finding that satisficing can be a very effective and efficient search strategy.} | |
| } | |
| @Inbook{Bearden:Murphy:2007, | |
| author = {Bearden, J. Neil and Murphy, Ryan O.}, | |
| title = {On Generalized Secretary Problems}, | |
| booktitle = {Uncertainty and Risk}, | |
| publisher = {Springer Berlin Heidelberg}, | |
| year = {2007}, | |
| pages = {187--205}, | |
| abstract = {This paper is composed of two related parts. In the first, we present a dynamic programming procedure for finding optimal policies for a class of sequential search problems that includes the well-known “secretary problem”. In the second, we propose a stochastic model of choice behavior for this class of problems and test the model with two extant data sets. We conclude that the previously reported bias for decision makers to terminate their search too early can, in part, be accounted for by a stochastic component of their search policies.} | |
| } | |
| @Article{Bearden:Rapoport:Murphy:2006, | |
| author = {Bearden, J. Neil and Rapoport, Amnon and Murphy, Ryan O.}, | |
| title = {Experimental Studies of Sequential Selection and Assignment with Relative Ranks}, | |
| journal = {Journal of Behavioral Decision Making}, | |
| volume = {19}, | |
| number = {}, | |
| year = {2006}, | |
| pages = {229--250}, | |
| abstract = {We study a class of sequential selection and assignment problems in which a decision maker (DM) must sequentially assign applicants to positions with the objective of minimizing expected cost. In modeling this class of problems, we assume that on each period the DM is only informed of the rank of the present applicant relative to the applicants that she previously observed and assigned. We first present the optimal decision policy that we subsequently use as a normative benchmark, and then report results from three experiments designed to study sequential assignment behavior. In comparing the aggregate results from all three experiments to the optimal decision policy, we identify a systematic bias, called the middleness bias, to over-assign applicants to intermediate positions. The results also reveal a strong bias for early applicants to be over-assigned to important positions.} | |
| } | |
| @Article{Beckmann:1990, | |
| author = {Beckmann, M. J.}, | |
| title = {Dynamic Programming and the Secretary Problem}, | |
| journal = {Computers and Mathematics with Applications}, | |
| volume = {19}, | |
| number = {11}, | |
| year = {1990}, | |
| pages = {25-28}, | |
| abstract = {In the secretary problem one seeks to maximize the probability of hiring the best of $N$ candidates who are interviewed in succession and must be accepted or rejected at the interview. A simple dynamic program is formulated and solved. Numerical results are given for secretary problems of small size.} | |
| } | |
| @Article{Bismuth:1977, | |
| author = {Bismuth, Jean-Michel}, | |
| title = {Sur un problème de {D}ynkin}, | |
| journal = {Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete}, | |
| volume = {39}, | |
| number = {1}, | |
| year = {1977}, | |
| month = {March}, | |
| pages = {31-53} | |
| } | |
| @Article{Bojdecki:1978, | |
| author = {Bojdecki, Tomasz}, | |
| title = {On Optimal Stopping of a Sequence of Independent Random Variables - Probability Maximizing Approach}, | |
| journal = {Stochastic Processes and their Applications}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {6}, | |
| number = {2}, | |
| year = {1978}, | |
| month = {December}, | |
| pages = {153--163}, | |
| abstract = {Let ξ1,ξ2,… be a sequence of independent, identically distributed r.v. with a continuous distribution function. Optimal stopping problems are considered for: (1) a finite sequence ξ1,…,ξN, (2) sequences (ξn−cn)nϵN and (max(ξ1,…,ξn) − cn)nϵN, where c is a fixed positive number, (3) the sequence (ξn)nϵN, where it is additionally assumed that ξ1,ξ2,… appear according to a Poisson process which is independent of {ξn}nϵN, and the decision about stopping must be made before some fixed moment T. The object of optimization is not (as it is in the classical formulation of optimal stopping problems) the expected value of the reward, but the probability that at the moment of stopping the reward attains its maximal value. It is proved that optimal stopping rules (in the above sense) for all problems exist, and their forms are found.} | |
| } | |
| @Article{Bradt:Johnson:Karlin:1956, | |
| author = {Bradt, R. N. and Johnson, S. M. and Karlin, S.}, | |
| title = {On Sequential Designs for Maximizing the Sum of $n$ Observations}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {27}, | |
| number = {4}, | |
| year = {1956}, | |
| month = {December}, | |
| pages = {1060--1074} | |
| } | |
| @Article{Broder:Etc:2009, | |
| author = {Broder, Andrei Z. and Kirsh, Adam and Kumar, Ravi and Mitzenmacher, Michael and Vassilvitzkii, Sergei}, | |
| title = {The Hiring Problem and Lake Wobegon Strategies}, | |
| journal = {{S}{I}{A}{M} Journal on Computing}, | |
| volume = {39}, | |
| number = {4}, | |
| year = {2009}, | |
| pages = {1233-1255}, | |
| abstract = {We introduce the hiring problem, in which a growing company continuously interviews and decides whether to hire applicants. This problem is similar in spirit but quite different from the well-studied secretary problem. Like the secretary problem, it captures fundamental aspects of decision making under uncertainty and has many possible applications. We analyze natural strategies of hiring above the current average, considering both the mean and the median averages; we call these Lake Wobegon strategies. Like the hiring problem itself, our strategies are intuitive, simple to describe, and amenable to mathematically and economically significant modifications. We demonstrate several intriguing behaviors of the two strategies. Specifically, we show dramatic differences between hiring above the mean and above the median. We also show that both strategies are intrinsically connected to the lognormal distribution, leading to only very weak concentration results, and the marked importance of the first few hires on the overall outcome.} | |
| } | |
| @Article{Bruss:1984, | |
| author = {Bruss, Thomas F.}, | |
| title = {A Unified Approach to a Class of Best Choice Problems with an Unknown Number of Options}, | |
| journal = {The Annals of Probability}, | |
| volume = {12}, | |
| number = {3}, | |
| year = {1984}, | |
| pages = {882-889} | |
| } | |
| @Article{Bruss:1988, | |
| author = {Bruss, Thomas F.}, | |
| title = {Invariant Record Processes and Applications to Best Choice Modelling}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {30}, | |
| number = {}, | |
| year = {1988}, | |
| pages = {303-316} | |
| } | |
| @Article{Bruss:2000, | |
| author = {Bruss, Thomas F.}, | |
| title = {Sum the Odds to One and Stop}, | |
| journal = {The Annals of Probability}, | |
| volume = {28}, | |
| number = {3}, | |
| year = {2000}, | |
| pages = {1384-1391}, | |
| abstract = {The objective of this paper is to present two theorems which are directly applicable to optimal stopping problems involving independent indicator functions. The proofs are elementary. One implication of the results is a convenient solution algorithm to obtain the optimal stopping rule and the value. We will apply it to several examples of sequences of independent indicators, including sequences of random length. Another interesting implication of the results is that the well-known asymptotic value $1/e$ for the classical best-choice problem is in fact a typical lower bound in a much more general class of problems.} | |
| } | |
| @Article{Bruss:2003, | |
| author = {Bruss, Thomas F.}, | |
| title = {A Note On Bounds for the Odds Theorem of Optimal Stopping}, | |
| journal = {The Annals of Probability}, | |
| volume = {31}, | |
| number = {4}, | |
| year = {2003}, | |
| pages = {1859-1861}, | |
| abstract = {The odds theorem gives a unified answer to a class of stopping problems on sequences of independent indicator functions. The success probability of the optimal rule is known to be larger than $Re^{−R}$, where $R$ defined in the theorem satisfies $R \geq 1$ in the more interesting case. The following findings strengthen this result by showing that $1/e$ is then a lower bound. Knowing that this is the best possible uniform lower bound motivates this addendum.} | |
| } | |
| @Article{Bruss:2005, | |
| author = {Bruss, Thomas F.}, | |
| title = {What Is Known About {R}obbins' Problem?}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {42}, | |
| year = {2005}, | |
| pages = {108-120} | |
| } | |
| @Article{Bruss:2010, | |
| author = {Bruss, F. Thomas}, | |
| title = {On a Class of Optimal Stopping Problems with Mixed Constraints}, | |
| journal = {Discrete Mathematics and Theoretical Computer Science}, | |
| volume = {12}, | |
| number = {2} | |
| year = {2010}, | |
| month = {January}, | |
| pages = {363--380}, | |
| abstract = {Let X(1),X(2),...,X(n) be independent, identically distributed uniform random variables on [0, 1]. We can observe the outcomes sequentially and must select online at least r of them, and, moreover, in expectation at least mu >= r. Here mu need not be integer. We see X(k) as the cost of selecting item k and want to minimize the expected total cost under the described combined (r, mu)-constraint. We will see that an optimal selection strategy exists on the set S(n) of all selection strategies for which the decision at instant k may depend on the value X(k), on the number N(k) of selections up to time k and of the number n - k of forthcoming observations. Let sigma(r,mu)(n) be the corresponding S(n)-optimal selection strategy and v(r,mu)(n) its value. The main goal of this paper is to determine these and to understand the limiting behavior of v(r,mu)(n). After discussion of the specific character of this combination of two types of constraints we conclude that the S(n)-problem has a recursive structure and solve it in terms of a double recursion. Our interest will then focus on the limiting behavior of nv(r,mu)(n) as n -> infinity. This sequence converges and its limit allows for the interpretation of a normalized limiting cost L (r, mu) of the (r, mu)-constraint. Our main result is that L(r, mu) = g(r) ((mu - r)(2)/(2)) where g(r) is the r(th) iterate of the function g(x) = 1 + x + root 1 + 2x. Our motivation to study mixed-constraints problems is indicated by several examples of possible applications. We also shortly discuss the intricacy of the expectational part of the constraint if we try to extend the class of strategies S n to the set of full-history-dependent and/or randomized strategies.} | |
| } | |
| @Article{Bruss:Delbaen:2001, | |
| author = {Bruss, Thomas F. and Delbaen, Freddy}, | |
| title = {Optimal Rules for the Sequential Selection of Monotone Subsequences of Maximum Expected Length}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {96}, | |
| number = {}, | |
| year = {2001}, | |
| pages = {313-342}, | |
| abstract = {This article presents new results on the problem of selecting (online) a monotone subsequence of maximum expected length from a sequence of i.i.d. random variables. We study the case where the variables are observed sequentially at the occurrence times of a Poisson process with known rate. Our approach is a detailed study of the integral equation which determines $v(t)$, the expected number (under the optimal strategy for time horizon $t$) of selected points $L_t^t$ up to time $t$. We first show that $v(t)$, $v^{\prime}(t)$ and $v^{\prime\prime}(t)$ exist everywhere on $\mathbb{R}^{+}$. [...] As an application, this result is used to extend a known result on the equivalence of a specific bin-packing problem with a certain subsequence problem. Our more personal interest in quick selection rules and their performance leads us also to the study of a class of convenient graph-rules. Known results on the concentration measure of record values suggest that the asymptotically best graph-rule should be the diagonal line rule, and we prove this intuition to be correct.} | |
| } | |
| @Article{Bruss:Delbaen:2004, | |
| author = {Bruss, Thomas F. and Delbaen, Freddy}, | |
| title = {A Central Limit Theorem for the Optimal Selection Process for Monotone Subsequences of Maximum Expected Length}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {114}, | |
| number = {}, | |
| year = {2004}, | |
| pages = {287-311}, | |
| abstract = {This article provides a refinement of the main results for the monotone subsequence selection problem [...]} | |
| } | |
| @Article{Bruss:Drmota:Louchard:1998, | |
| author = {Bruss, Thomas F. and Drmota, Michael and Louchard, Guy}, | |
| title = {The Complete Solution of the Competitive Rank Selection Problem}, | |
| journal = {Algorithmica}, | |
| publisher = {Springer-Verlag}, | |
| volume = {22}, | |
| number = {4}, | |
| year = {1988}, | |
| pages = {413-447} | |
| } | |
| @Article{Bruss:Ferguson:2002, | |
| author = {Bruss, F. Thomas and Ferguson, Thomas S.}, | |
| title = {High-Risk and Competitive Investment Models}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {12}, | |
| number = {4}, | |
| year = {2002}, | |
| month = {November}, | |
| pages = {1202-1226} | |
| } | |
| @Article{Bruss:Louchard:1998, | |
| author = {Bruss, Thomas F. and Louchard, Guy}, | |
| title = {Sharp Bounds for Winning Probabilities in the Competitive Rank Selection Problem}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {35}, | |
| year = {1998}, | |
| pages = {1007-1011} | |
| } | |
| @Article{Bruss:Paindaveine:2000, | |
| author = {Bruss, Thomas F. and Paindaveine, Davy}, | |
| title = {Selecting a Sequence of Last Successes in Independent Trials}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {37}, | |
| year = {2000}, | |
| pages = {389-399} | |
| } | |
| @Article{Bruss:Rogers:1991, | |
| author = {Bruss, Thomas F. and Rogers, L. C. G.}, | |
| title = {Embedding Optimal Selection Problems in a Poisson Process}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {38}, | |
| number = {}, | |
| year = {1991}, | |
| pages = {267-278} | |
| } | |
| @Article{Bruss:Samuels:1987, | |
| author = {Bruss, Thomas F. and Samuels, Stephen M.}, | |
| title = {A Unified Approach to a Class of Optimal Selection Problems with an Unknown Number of Options}, | |
| journal = {Annals of Probability}, | |
| volume = {15}, | |
| number = {2}, | |
| year = {1987}, | |
| pages = {824-830}, | |
| abstract = {In the so-called Secretary Problem, if an unknown number, $N$, of options arrive at i.i.d. times with a known continuous distribution, their ignorance of how many options there are becomes irrelevant: The optimal rules for infinitely many options is shown to be minimax with respect to all possible distributions of $N$, nearly optimal whenever $N$ is likely to be large, and formal Bayes against a noninformative prior. These results hold whatever the loss function.} | |
| } | |
| @Article{Bruss:Samuels:1990, | |
| author = {Bruss, Thomas F. and Samuels, Stephen M.}, | |
| title = {Conditions for Quasi-Stationarity of the Bayes Rule in Selection Problems with an Unknown Number of Rankable Options}, | |
| journal = {Annals of Probability}, | |
| volume = {18}, | |
| number = {2}, | |
| year = {1990}, | |
| pages = {877-886}, | |
| abstract = {In the so-called Secretary Problem, if an unknown number, $N$, of options arrive at i.i.d. times with a known continuous distribution, then only the geometric, among proper distributions on $N$, has the property that the stopping risk depends just on the elapsed time and not on the number of arrivals so far. But even with such a prior, the optimal rule may, in general, depend on the number of arrivals so far. The optimal rule is closely related to the optimal policy in the Gianini and Samuels infinite secretary problem, except for a linear change in the time scale which depends only on the parameter of the prior, and not on the loss function.} | |
| } | |
| @Article{Cabilio:1977, | |
| author = {Cabilio, Paul}, | |
| title = {Sequential Estimation in {B}ernoulli Trials}, | |
| journal = {The Annals of Statistics}, | |
| volume = {5}, | |
| number = {2}, | |
| year = {1977}, | |
| pages = {342--356}, | |
| abstract = {The sequential estimation of p, the probability of success in a sequence of Bernoulli trials, is considered for the case where loss is taken to be symmetrized relative squared error of estimation, plus a fixed cost $c$ per observation. Using $s_n/n$ as a terminal estimator of $p$, where $s_n$ is the number of successes in $n$ trials, a heuristic rule is derived and shown to perform well for any fixed $0 < p < 1$ as $c \rightarrow 0$. However for any fixed $c > 0$, this rule performs badly for $p$ close to $0$ or $1$. To overcome this difficulty a uniform prior on $p$ is introduced, and the optimal Bayes procedure is shown to exist and to have bounded sample size. The optimal Bayes risk is shown to be $\~ 2\pic^{1/2}$ as $c \rightarrow 0$, and is computed for various values of $c$, along with the expected loss for various values of $p$.} | |
| } | |
| @Article{Campbell:Samuels:1981, | |
| author = {Campbell, Gregory and Samuels, Stephen M.}, | |
| title = {Choosing the Best of the Current Crop}, | |
| journal = {Advances in Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {13}, | |
| number = {3}, | |
| year = {1981}, | |
| month = {September}, | |
| pages = {510--532} | |
| } | |
| @Article{Chen:Nair:Odlyzko:Shepp:Vardi:1984, | |
| author = {Chen, Robert W. and Nair, V. N. and Odlyzko, A. M. and Shepp, Larry A. and Vardi, Y.}, | |
| title = {Optimal Sequential Selection of $N$ Random Variables Under a Constraint}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {21}, | |
| number = {3}, | |
| year = {1984}, | |
| month = {September}, | |
| pages = {537--547}, | |
| abstract = {We observe a sequence $\{X_k\}_k \geq 1$ of i.i.d. non-negative random variables one at a time. After each observation, we select or reject the observed variable. A variable that is rejected may not be recalled. We want to select $N$ variables as soon as possible subject to the constraint that the sum of the $N$ selected variables does not exceed some prescribed value $C>0$. In this paper, we develop a sequential selection procedure that minimizes the expected number of observed variables, and we study some of its properties. We also consider the situation where $N \rightarrow \infty$ and $C/N \rightarrow \alpha > 0$. Some applications are briefly discussed.} | |
| } | |
| @Article{Chen:Rosenberg:Shepp:1997, | |
| author = {Chen, Robert W. and Rosenberg, Burton and Shepp, Larry A.}, | |
| title = {A Secretary Problem with Two Decision Makers}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {34}, | |
| number = {4}, | |
| year = {1997}, | |
| month = {December}, | |
| pages = {1068--1074}, | |
| abstract = {$n$ applicants of similar qualification are on an interview list and their salary demands are from a known and continuous distribution. Two managers, I and II, will interview them one at a time. Right after each interview, manager I always has the first opportunity to decide to hire the applicant or not unless she has hired one already. If manager I decides not to hire the current applicant, then manager II can decide to hire the applicant or not unless he has hired one already. If both managers fail to hire the current applicant, they interview the next applicant, but both lose the chance of hiring the current applicant. If one of the managers does hire the current one, then they proceed with interviews until the other manager also hires an applicant. The interview process continues until both managers hire an applicant each. However, at the end of the process, each manager must have hired an applicant. In this paper, we first derive the optimal strategies for them so that the probability that the one he hired demands less salary than the one hired by the other does is maximized. Then we derive an algorithm for computing manager II's winning probability when both managers play optimally. Finally we show that manager II's winning probability is strictly increasing in $n$, is always less than $c$, and converges to $c$ as $n$ $\rightarrow$ $\infty$, where $c=0.3275624139...$ is a solution of the equation $\ln(2) + x \ln(x) = x$.} | |
| } | |
| @Article{Chen:Starr:1980, | |
| author = {Chen, Wen-chen and Starr, Norman}, | |
| title = {Optimal Stopping in an Urn}, | |
| journal = {The Annals of Probability}, | |
| volume = {8}, | |
| number = {3}, | |
| year = {1980}, | |
| pages = {451-464}, | |
| abstract = {An urn contains $N$ objects, labelled with the integer $1,...,N$. One object is removed at a time, without replacement. If after $n$ draws the largest number which has been observed is $m_n$, and the process is terminated, we receive a payoff $f(n,m_n)$. For payoff functions $f$ in a certain class, the optimal time to stop is with draw $T_f = inf\{n \geq 0: m_n - n \geq j_n\}$, where the $j_n$ are computable from a simple algorithm, which permits also exact computation of the value $V_f = E \{f(\tau_{f}, m_{\tau_f})\}$. We also study the behavior of $V$ when $N$ is large in special cases.} | |
| } | |
| @Article{Chow:1967, | |
| author = {Chow, Yuan Shih}, | |
| title = {On the Expected Value of a Stopped Submartingale}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {38}, | |
| number = {2}, | |
| year = {1967}, | |
| month = {April}, | |
| pages = {608--609} | |
| } | |
| @Article{Chow:Moriguti:Robbins:Samuels:1964, | |
| author = {Chow, Yuan Shih and Moriguti, S. and Robbins, Herbert and Samuels, S. M.}, | |
| title = {Optimal Selection Based on Relative Ranks (the ``Secretary Problem'')}, | |
| journal = {Israel Journal of Mathematics}, | |
| publisher = {Springer-Verlag}, | |
| volume = {2}, | |
| number = {2}, | |
| year = {1964}, | |
| month = {June}, | |
| pages = {81-90}, | |
| abstract = {$n$ rankable persons appear sequentially in random order. At the $i$th stage we observe the relative ranks of the first $i$ persons to appear, and must either select the $i$th person, in which case the process stops, or pass on to the next stage. For that stopping rule which minimizes the expectation of the absolute rank of the person selected, it is shown that as $n\rightarrow\infty$ this tends to the value | |
| $\Pi_{j=1}^{\infty}\left(\frac{j+2}{j}\right)^{1/j+1} \simeq 3.8695$.} | |
| } | |
| @Inproceedings{Chow:Robbins:1961, | |
| author = {Chow, Yuan Shih and Robbins, Herbert}, | |
| title = {A Martingale System Theorem and Applications}, | |
| booktitle = {Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics}, | |
| publisher = {University of California Press}, | |
| year = {1961}, | |
| pages = {93--104} | |
| } | |
| @Article{Chow:Robbins:1965, | |
| author = {Chow, Yuan Shih and Robbins, Herbert}, | |
| title = {On Optimal Stopping Rules For $s_{n}/n$}, | |
| journal = {Illinois Journal of Mathematics}, | |
| volume = {9}, | |
| number = {3}, | |
| year = {1965}, | |
| month = {September}, | |
| pages = {444--454} | |
| } | |
| @Inproceedings{Chow:Robbins:1967a, | |
| author = {Chow, Yuan Shih and Robbins, Herbert}, | |
| title = {On Values Associated with a Stochastic Sequence}, | |
| booktitle = {Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics}, | |
| publisher = {University of California Press}, | |
| year = {1967}, | |
| pages = {427--440} | |
| } | |
| @Inproceedings{Chow:Robbins:1967b, | |
| author = {Chow, Yuan Shih and Robbins, Herbert}, | |
| title = {A Class of Optimal Stopping Problems}, | |
| booktitle = {Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics}, | |
| publisher = {University of California Press}, | |
| year = {1967}, | |
| pages = {419--426} | |
| } | |
| @Article{Chow:Robbins:Teicher:1965, | |
| author = {Chow, Yuan Shih and Robbins, Herbert and Teicher, Henry}, | |
| title = {Moments of Randomly Stopped Sums}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {36}, | |
| number = {3}, | |
| year = {1965}, | |
| month = {June}, | |
| pages = {789-799} | |
| } | |
| @Article{Chudjakow:Riedel:2013, | |
| author = {Chudjakow, Tatjana and Riedel, Frank}, | |
| title = {The Best Choice Problem Under Ambiguity}, | |
| journal = {Economic Theory}, | |
| volume = {54}, | |
| number = {}, | |
| year = {2013}, | |
| pages = {77--97}, | |
| abstract = {We model and solve best choice problems in the multiple prior framework: An ambiguity averse decision maker aims to choose the best among a fixed number of applicants that appear sequentially in a random order. The agent faces ambiguity about the probability that a candidate -- a relatively top applicant -- is actually best among all applicants. We show that our model covers the classical secretary problem, but also other interesting classes of problems. We provide a closed form solution of the problem for time-consistent priors using backward induction. As in the classical case, the derived stopping strategy is simple. Ambiguity can lead to substantial differences to the classical threshold rule.} | |
| } | |
| @Article{Chun:1996a, | |
| author = {Chun, Young Hak}, | |
| title = {Rank-Based Selection Strategies for the Random Walk Process}, | |
| journal = {European Journal of Operations Research}, | |
| volume = {96}, | |
| number = {}, | |
| year = {1996}, | |
| pages = {417--427}, | |
| abstract = {In many decision situations such as hiring a secretary, selling an asset, or seeking a job, the value of each offer, applicant, or choice is assumed to be an independent, identically distributed random variable. In this paper, we consider a special case where the observations are auto-correlated as in the random walk model for stock prices. For a given random walk process of $n$ observations, we explicitly compute the probability that the $j$-th observation in the sequence is the maximum or minimum among all $n$ observations. Based on the probability distribution of the rank, we derive several distribution-free selection strategies under which the decision maker's expected utility of selecting the best choice is maximized. We show that, unlike in the classical secretary problem, evaluating more choices in the random walk process does not increase the likelihood of successfully selecting the best.} | |
| } | |
| @Article{Chun:1996b, | |
| author = {Chun, Young Hak}, | |
| title = {Selecting the Best Choice in the Weighted Secretary Problem }, | |
| journal = {European Journal of Operational Research}, | |
| volume = {92}, | |
| number = {1}, | |
| year = {1996}, | |
| pages = {135--147}, | |
| abstract = {In the sequential evaluation and selection problem with n applicants, we assume that a decision maker has some prior information about each applicant so that unequal weights may be assigned to each applicant according to his or her likelihood of being the best among all applicants. Assuming that the pre-assigned weights are available in advance, we derive the optimal selection strategy that maximizes the probability of selecting the best among all applicants. For the case where the decision maker is permitted to rearrange the sequence in which applicants are evaluated, we further propose a simple heuristic procedure to the problem of optimally ordering the sequence of evaluations. Based on a pairwise comparison matrix and a goal programming procedure, we also propose a method that easily computes the weights in a practical situation.} | |
| } | |
| @Article{Chun:1997, | |
| author = {Chun, Young Hak}, | |
| title = {Rank-Based Selection Strategies for the Random Walk Process }, | |
| journal = {European Journal of Operational Research}, | |
| volume = {96}, | |
| number = {2}, | |
| year = {1997}, | |
| pages = {417--427}, | |
| abstract = {In many decision situations such as hiring a secretary, selling an asset, or seeking a job, the value of each offer, applicant, or choice is assumed to be an independent, identically distributed random variable. In this paper, we consider a special case where the observations are auto-correlated as in the random walk model for stock prices. For a given random walk process of n observations, we explicitly compute the probability that the j-th observation in the sequence is the maximum or minimum among all n observations. Based on the probability distribution of the rank, we derive several distribution-free selection strategies under which the decision maker's expected utility of selecting the best choice is maximized. We show that, unlike in the classical secretary problem, evaluating more choices in the random walk process does not increase the likelihood of successfully selecting the best.} | |
| } | |
| @Article{Chun:1999, | |
| author = {Chun, Young Hak}, | |
| title = {Selecting the best choice in the full information group interview problem }, | |
| journal = {European Journal of Operational Research}, | |
| volume = {119}, | |
| number = {3}, | |
| year = {1999}, | |
| pages = {635--651}, | |
| abstract = {We consider the problem of selecting the single best choice when several groups of choices are presented sequentially for evaluation. In the so-called group interview problem, we assume that the values of choices are random observations from a known distribution function and derive the optimal search strategy that maximizes the probability of selecting the best among all choices. Under the optimal search strategy derived by means of a dynamic programming technique, a decision maker simply selects the best choice in the group under consideration if its value is higher than the pre-specified decision value for that group. We also consider the optimal ordering strategy for the case where the decision maker is permitted to rearrange the sequence of groups for evaluation. We show that the optimal search and ordering strategies can be applied to many sequential decision problems such as the store location problem.} | |
| } | |
| @Article{Chun:2001, | |
| author = {Chun, Young Hak}, | |
| title = {Optimal partitioning of groups in selecting the best choice }, | |
| journal = {Computers and Operations Research}, | |
| volume = {28}, | |
| number = {14}, | |
| year = {2001}, | |
| pages = {1367--1386}, | |
| abstract = {This article deals with the group interview problem, in which each group contains several alternatives and each group of alternatives is presented and evaluated sequentially over time. We derive the optimal selection strategy for the group interview problem with a general utility function. Among the various types of utility function, we focus on the best choice problem, in which our utility is one if we successfully select the best choice and zero otherwise. We derive a simple selection rule called the optimal partitioning strategy in which the decision-maker divides the entire groups into two disjoint sets and, after evaluating the choices in the first set, chooses the relatively best choice available for the first time in the second set. Because the selected choice is not necessarily the absolutely best choice, we also consider the probability distribution of the actual rank of the choice selected under the partitioning strategy. Scope and purpose In many managerial decision situations such as buying a car, selling a house, or searching for a job, several alternatives are presented sequentially and an accept-or-reject decision is made immediately after evaluating each alternative. The classical secretary problem and its extensions have been successfully applied to such a sequential search and selection problem. This article deals with a more generalized version of the secretary problem, called the group interview problem, in which several groups of alternatives are presented and evaluated sequentially over time. Based on a stochastic dynamic programming approach, we propose the optimal selection strategy for the group interview problem with various types of the decision-maker's utility function. There are many potential applications of the group interview problem, including consumer search and purchase process, job search problem, sequential assignment of batch jobs, and so on.} | |
| } | |
| @Article{Chun:2015, | |
| author = {Young H. Chun}, | |
| title = {Multi-attribute sequential decision problem with optimizing and satisficing attributes }, | |
| journal = {European Journal of Operational Research}, | |
| volume = {243}, | |
| number = {1}, | |
| year = {2015}, | |
| pages = {224--232}, | |
| abstract = {We deal with the multi-attribute decision problem with sequentially presented decision alternatives. Our decision model is based on the assumption that the decision-maker has a major attribute that must be “optimized” and minor attributes that must be “satisficed”. In the vendor selection problem, for example, the product price could be the major factor that should be optimized, while the product quality and delivery time could be the minor factors that should satisfy certain aspiration levels. We first derive the optimal selection strategy for the discrete-time case in which one alternative is presented at each time period. The discrete-time model is then extended to the continuous-time case in which alternatives are presented sequentially at random times. A numerical example is used to analyze the effects of the satisficing condition and the uncertainty on the optimal selection strategy.} | |
| } | |
| @Article{Chun:Sumichrast:2006, | |
| author = {Young H. Chun and Robert T. Sumichrast}, | |
| title = {A rank-based approach to the sequential selection and assignment problem }, | |
| journal = {European Journal of Operational Research}, | |
| volume = {174}, | |
| number = {2}, | |
| year = {2006}, | |
| pages = {1338--1344}, | |
| abstract = {In the classical sequential assignment problem, ``machines'' are to be allocated sequentially to ``jobs'' so as to maximize the expected total return, where the return from an allocation of job j to machine k is the product of the value xj of the job and the weight pk of the machine. The set of m machines and their weights are given ahead of time, but n jobs arrive in sequential order and their values are usually treated as independent, identically distributed random variables from a known univariate probability distribution with known parameter values. In the paper, we consider a rank-based version of the sequential selection and assignment problem that minimizes the sum of weighted ranks of jobs and machines. The so-called “secretary problem” is shown to be a special case of our sequential assignment problem (i.e., $m = 1$). Due to its distribution-free property, our rank-based assignment strategy can be successfully applied to various managerial decision problems such as machine scheduling, job interview, kidney allocations for transplant, and emergency evacuation plan of patients in a mass-casualty situation.} | |
| } | |
| @Article{Cowan:Zabczyk:1978, | |
| author = {Cowan, R. and Zabczyk, J.}, | |
| title = {An Optimal Selection Problem Associated With the Poisson Process}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {23}, | |
| number = {3}, | |
| year = {1978}, | |
| month = {}, | |
| pages = {584--592}, | |
| abstract = {A generalization in continuous time of the secretary problem.} | |
| } | |
| @Inbook{Darling:1986, | |
| author = {Darling, Donald A.}, | |
| title = {Convergence Rates for Iterative Solutions to Optimal Stopping Problems}, | |
| booktitle = {Adaptive statistical procedures and related topics}, | |
| series = {Lecture Notes--Monograph Series}, | |
| editor = {Van Ryzin, John}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {8}, | |
| year = {1986}, | |
| pages = {18--28} | |
| } | |
| @Inproceedings{Das:Kamenica:2005, | |
| author = {Das, Sanmay and Kamenica, Emir}, | |
| title = {Two-Sided Bandits and the Dating Market}, | |
| booktitle = {Proceedings of the Nineteenth International Joint Conferences on Artificial Intelligence (2005}, | |
| year = {2005}, | |
| pages = {947--952}, | |
| abstract = {We study the decision problems facing agents in repeated matching environments with learning, or two-sided bandit problems, and examine the dat- ing market, in which men and women repeatedly go out on dates and learn about each other, as an ex- ample. We consider three natural matching mecha- nisms and empirically examine properties of these mechanisms, focusing on the asymptotic stability of the resulting matchings when the agents use a simple learning rule coupled with an ε-greedy ex- ploration policy. Matchings tend to be more stable when agents are patient in two different ways — if they are more likely to explore early or if they are more optimistic. However, the two forms of pa- tience do not interact well in terms of increasing the probability of stable outcomes. We also define a notion of regret for the two-sided problem and study the distribution of regrets under the different matching mechanisms.} | |
| } | |
| @Article{David:Yechiali:1995, | |
| author = {David, Israel and Yechiali, Uri}, | |
| title = {One-Attribute Sequential Assignment Match Processes in Discrete Time}, | |
| journal = {Operations Research}, | |
| volume = {43}, | |
| number = {5}, | |
| year = {1995}, | |
| month = {}, | |
| pages = {879-884}, | |
| abstract = {We consider a sequential matching problem where $M$ offers arrive in a random stream and are to be sequentially assigned to $N$ waiting candidates. Each candidate, as well as each offer, is characterized by a random attribute drawn from a known discrete- valued probability distribution function. An assignment of an offer to a candidate yields a (nominal) reward $R > 0$ if they match, and a smaller reward $r \leq R$ if they do not. Future rewards are discounted at a rate $0 \leq \alpha \leq 1$. We study several cases with various assumptions on the problem parameters and on the assignment regime and derive optimal policies that maximize the total (discounted) reward. The model is related to the problem of donor-recipient assignment in live organ transplants, studied in an earlier work.} | |
| } | |
| @Article{Derman:Lieberman:Ross:1972, | |
| author = {Derman, Cyrus and Lieberman, Gerald J. and Ross, Sheldon M.}, | |
| title = {A Sequential Stochastic Assignment Problem}, | |
| journal = {Management Science}, | |
| volume = {18}, | |
| number = {7}, | |
| year = {1972}, | |
| month = {March}, | |
| pages = {7 pages} | |
| } | |
| @Article{Dhariyal:Dudewicz:1981, | |
| author = {Dhariyal, Ishwari D. and Dudewicz, Edward J.}, | |
| title = {Optimal Selection from a Finite Sequence with Sampling Cost}, | |
| journal = {Journal of the American Statistical Association}, | |
| volume = {76}, | |
| number = {376}, | |
| year = {1981}, | |
| month = {December}, | |
| pages = {952-959}, | |
| abstract = {Two variations of the problem of choosing the largest of $N$ independent and identically distributed (iid) random variables with sampling cost are studied. In the first case it is assumed that the underlying distribution is continuous and known, but the information obtained by sampling is whether the sampled variable is larger or smaller than some given level. In the second case it is assumed that the distribution of the random variable is continuous but unknown, and the information obtained is the rank of the sampled variable relative to the other variables already in the sample. In each case both the optimal strategy and the distribution of the stopping variable are discussed.} | |
| } | |
| @Article{Domansky:2000, | |
| author = {Domansky, V. K.}, | |
| title = {Randomized Optimal Stopping Times for a Class of Stopping Games}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {46}, | |
| number = {4}, | |
| year = {2000}, | |
| pages = {708-717} | |
| } | |
| @Article{Dynkin:1962, | |
| author = {Dynkin, Eugene B.}, | |
| title = {The Optimum Choice of the Instant for Stopping a {M}arkov Process}, | |
| journal = {Soviet Math. Dokl}, | |
| volume = {4}, | |
| year = {1962} | |
| } | |
| @Article{Dynkin:1969, | |
| author = {Dynkin, Eugene B.}, | |
| title = {Game Variant of a Problem On Optimal Stopping}, | |
| journal = {Soviet Math. Dokl}, | |
| volume = {10}, | |
| number = {2}, | |
| year = {1969} | |
| } | |
| @Article{Ekstrom:Peskir:2008, | |
| author = {Ekstrom, Erik and Peskir, Goran}, | |
| title = {Optimal Stopping Games for {M}arkov Processes}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {47}, | |
| number = {2}, | |
| year = {2008}, | |
| pages = {684-702} | |
| } | |
| @Article{Ekstrom:Villeneuve:2006, | |
| author = {Ekstrom, Erik and Villeneuve, Stephane}, | |
| title = {On the Value of Optimal Stopping Games}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {16}, | |
| number = {3}, | |
| year = {2006}, | |
| month = {August}, | |
| pages = {1576-1596}, | |
| abstract = {We show, under weaker assumptions than in the previous literature, that a perpetual optimal stopping game always has a value. We also show that there exists an optimal stopping time for the seller, but not necessarily for the buyer. Moreover, conditions are provided under which the existence of an optimal stopping time for the buyer is guaranteed. The results are illustrated explicitly in two examples.} | |
| } | |
| @Article{Elbakidze:1974, | |
| author = {Elbakidze, N V.}, | |
| title = {Construction of the Cost and Optimal Policies in a Game Problem of Stopping a {M}arkov Process}, | |
| journal = {Theory of Probability and Its Applications}, | |
| volume = {21}, | |
| number = {1}, | |
| year = {1974}, | |
| pages = {163--168} | |
| } | |
| @Article{Enns:1970a, | |
| author = {Enns, Von E. G.}, | |
| title = {The Decision Process for Maximizing the Probability of Obtaining the Random Variable Nearest to an Arbitrary Real Number}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| volume = {41}, | |
| number = {5}, | |
| year = {1970}, | |
| pages = {1466-1471}, | |
| abstract = {Warning! In 1973, Enns wrote that ``These results are in error.''} | |
| } | |
| @Article{Enns:1970b, | |
| author = {Enns, Von E. G.}, | |
| title = {The Optimum Strategy for Choosing the Maximum N Independent Random Variables}, | |
| journal = {Unternehmensforschung}, | |
| publisher = {Physica-Verlag}, | |
| volume = {14}, | |
| number = {1}, | |
| year = {1970}, | |
| pages = {89-96}, | |
| abstract = {In this paper the problem of choosing the maximum of a given number of Random Variables (R.V.s) has been considered when they are presented sequentially and their distribution is known. Only one R.V. can be accepted and in each case when a R.V. is presented it is either accepted or rejected, never to be accepted later. The strategy which maximizes the probability of obtaining the largest R.V. is obtained and called the optimum strategy. When this optimum strategy is followed, the probability of choosing any particular order statistic is determined and shown to be independent of the distribution of the R.V.s. The asymptotic distribution of the order statistic chosen is found and selected probabilities listed in the Tables. Also included is a table of the optimum strategy and a graph of the number of R.V.s to be sampled if one wishes the R.V. chosen to be in the top $\alpha$ fraction of the population with a given probability.} | |
| } | |
| @article{Enns:1975, | |
| author = {Enns, E. G.}, | |
| title = {Selecting the Maximum of a Sequence with Imperfect Information}, | |
| journal = {Journal of the American Statistical Association}, | |
| publisher = {Taylor and Francis, Ltd. on behalf of the American Statistical Association}, | |
| volume = {70}, | |
| number = {351}, | |
| year = {1975}, | |
| month = {September}, | |
| pages = {640--643}, | |
| abstract = {N independent and identically distributed random variables are sampled sequentially from a known continuous distribution. The information obtained is whether the sampled random variable is greater or less than some level specified by the sampler. The optimal strategy for maximizing the probability of selecting the largest member of the sequence is obtained and tabulated for N ≤ 25. When following the optimal strategy, the expected value of the number sampled is shown to equal N times the probability that the maximum is attained. This remains true for a reduced set of decision levels, provided the reduced set of levels are optimal.} | |
| } | |
| @Article{Enns:Ferenstein:1985, | |
| author = {Enns, E. G. and Ferenstein, Elzbieta}, | |
| title = {The Horse Game}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {28}, | |
| number = {1}, | |
| year = {1985}, | |
| month = {March}, | |
| pages = {51-62}, | |
| abstract = {Two Players...} | |
| } | |
| @Article{Enns:Ferenstein:1987, | |
| author = {Enns, E.G. and Ferenstein, Elzbieta}, | |
| title = {On a Multi-Person Time-Sequential Game with Priorities}, | |
| journal = {Sequential Analysis}, | |
| volume = {6}, | |
| number = {3}, | |
| year = {1987}, | |
| pages = {239-256}, | |
| abstract = {Two Players...} | |
| } | |
| @Article{Enns:Ferenstein:1990, | |
| author = {Enns, E.G. and Ferenstein, Elzbieta}, | |
| title = {A Competitive Best-Choice Problem with Poisson Arrivals}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {27}, | |
| year = {1990}, | |
| month = {}, | |
| pages = {333-342}, | |
| abstract = {Two Players...} | |
| } | |
| @Article{Eriksson:Sjostrand:Strimling:2007, | |
| author = {Eriksson, Kimmo and Sjostrand, Jonas and Strimling, Pontus}, | |
| title = {Optimal Expected Rank in a Two-Sided Secretary Problem}, | |
| journal = {Operations Research}, | |
| volume = {55}, | |
| number = {5}, | |
| year = {2007}, | |
| month = {September-October}, | |
| pages = {921-931}, | |
| abstract = {In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than $N$ interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the $N$ potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of $N$ (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.} | |
| } | |
| @Article{Eriksson:Sjostrand:Strimling:2008, | |
| author = {Eriksson, Kimmo and Sjostrand, Jonas and Strimling, Pontus}, | |
| title = {Asymmetric Equilibria in Dynamic Two-Sided Matching Markets with Independent Preferences}, | |
| journal = {International Journal of Game Theory}, | |
| volume = {36}, | |
| number = {}, | |
| year = {2008}, | |
| pages = {421-440}, | |
| abstract = {A fundamental fact in two-sided matching is that if a market allows several stable outcomes, then one is optimal for all men in the sense that no man would prefer another stable outcome. We study a related phenomenon of asymmetric equilibria in a dynamic market where agents enter and search for a mate for at most n rounds before exiting again. Assuming independent preferences, we find that this game has multiple equilibria, some of which are highly asymmetric between sexes. We also investigate how the set of equilibria depends on a sex difference in the outside option of not being mated at all.} | |
| } | |
| @Article{Fakeev:1968, | |
| author = {Fakeev, A. G.}, | |
| title = {On Necessary Conditions for Optimality in Sequential Decision Problems}, | |
| journal = {Theory of Probability and Its Applications}, | |
| volume = {14}, | |
| number = {4}, | |
| year = {1968}, | |
| pages = {710-713} | |
| } | |
| @Article{Feng:Hartman:2013, | |
| author = {Feng, Tianke and Hartman, Joseph C.}, | |
| title = {The Sequential Stochastic Assignment Problem with Postponement Options}, | |
| journal = {Probability in the Engineering and Informational Sciences}, | |
| volume = {27}, | |
| number = {}, | |
| year = {2013}, | |
| pages = {25-51}, | |
| abstract = {The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources.} | |
| } | |
| @Article{Faller:Ruschendorf:2012, | |
| author = {Faller, Andreas and Ruschendorf, Ludger}, | |
| title = {Approximate Solutions of Best Choice Problems}, | |
| journal = {Electronic Journal of Probability}, | |
| volume = {17}, | |
| number = {54}, | |
| year = {2012}, | |
| pages = {1-22}, | |
| abstract = {We consider the full information best choice problem from a sequence $X_1$, ..., $X_n$ of independent random variables. Under the basic assumption of convergence of the corresponding embedded point processes in the plane to a Poisson process we establish that the optimal choice problem can be approximated by the optimal choice problem in the limiting Poisson process. This allows to derive approximations to the optimal choice probability and also to determine approximately optimal stopping times. An extension of this result to the best $m$-choice problem is also given.} | |
| } | |
| @Article{Ferenstein:1992, | |
| author = {Ferenstein, Elzbieta}, | |
| title = {Randomized Stopping Games and {M}arkov Market Games}, | |
| journal = {Contemporary Mathematics}, | |
| publisher = {American Mathematical Society}, | |
| volume = {125}, | |
| year = {1992}, | |
| pages = {119-133}, | |
| abstract = {We consider two-person non-zero-sum sequential games with priorities. Two players observe successively states of a nonterminating homogeneous Markov chain. One state may be selected in a sequential way by one of the players, with a priority in making decisions (to select or to reject the observed state) for player 1. Player 2 may select the current state if and only if there has not been a selection at an earlier stage and Player 1 has rejected it. Each of the players gets a reward depending on the accepted state and on who has made a selection. A characterization of Nash solutions with respect to player's mean rewards, as well as some examples, are presented. The considered games may be related to bivariate optimal stopping problems with constraints. The paper extends results of Enn and Ferenstein (1987) and Ferenstein (1990).} | |
| } | |
| @Incollection{Ferenstein:2004, | |
| author = {Ferenstein, Elzbieta}, | |
| title = {On Randomized Stopping Games}, | |
| booktitle = {Advances in Dynamic Games}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| editor = {Nowak, AndrzejS. and Szajowski, Krzysztof}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {7}, | |
| year = {2004}, | |
| pages = {211-220}, | |
| abstract = {The paper is concerned with two-person nonzero-sum stopping games in which pairs of randomized stopping times are game strategies. For a general form of reward functions, existence of Nash equilibrium strategies is proved under some restrictions for three types of games: quasi-finite-horizon, random- horizon and infinite-horizon games.} | |
| } | |
| @Article{Ferenstein:2007, | |
| author = {Ferenstein, Elzbieta}, | |
| title = {Randomized Stopping Games and {M}arkov Market Games}, | |
| journal = {Mathematical Methods of Operations Research}, | |
| volume = {66}, | |
| number = {}, | |
| year = {2007}, | |
| pages = {531-544}, | |
| abstract = {The paper is concerned with two types of games: m-person nonzero-sum noncooperative sequential games in which randomized stopping times are players strategies and some specific stochastic games interpreted as market games (or some econometric models). In the former, players payoffs are their utility functions (in particular case) dependent on a state of the observed sequentially discrete-time Markov process at the random moment of stopping. These games are generalizations of the stopping game formulated by Dynkin (1969) as an example of optimal stopping of random sequences. In the latter, players control transition probability law of a Markov chain so as to stop it at a random moment with the aim to maximize their expected utilities dependent on the current state of the process and on the collection of players who have decided to stop it.} | |
| } | |
| @Incollection{Ferenstein:Krasnosielska:2009, | |
| author = {Ferenstein, Elzbieta and Krasnosielska, Anna}, | |
| title = {{N}ash Equilibrium in a Game Version of the {E}lfving Problem}, | |
| booktitle = {Advances in Dynamic Games and Their Applications}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| editor = {Pourtallier, Odile and Gaitsgory, Vladimir and Bernhard, Pierre}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {10}, | |
| year = {2009}, | |
| pages = {1--16}, | |
| abstract = {Multi-person stopping games with a finite and infinite horizon, players' priorities, and observed rewards at jump times of a Poisson process are considered. The existence of a Nash equilibrium is proved and its explicit form is obtained for special classes of reward sequences. Our game is a generalization of the Elfving stopping time problem to the case of many players and modification of multi-person stopping games with priorities.} | |
| } | |
| @Article{Ferguson:1989, | |
| author = {Ferguson, Thomas S.}, | |
| title = {Who Solved the Secretary Problem?}, | |
| journal = {Statistical Science}, | |
| volume = {4}, | |
| number = {3}, | |
| year = {1989}, | |
| month = {August}, | |
| pages = {282-289} | |
| } | |
| @Incollection{Ferguson:1992, | |
| author = {Ferguson, Thomas S.}, | |
| title = {Best-Choice Problems with Dependent Criteria}, | |
| booktitle = {Strategies for Sequential Search and Selection in Real Time}, | |
| editor = {F. Thomas Bruss, Thomas Shelburne Ferguson}, | |
| publisher = {American Mathematical Society}, | |
| series = {Contemporary Mathematics, Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held June 21-27, 1990}, | |
| volume = {125}, | |
| year = {1992}, | |
| month = {January}, | |
| pages = {135--151} | |
| } | |
| @Incollection{Ferguson:2004, | |
| author = {Ferguson, Thomas S.}, | |
| title = {Selection by Committee}, | |
| booktitle = {Advances in Dynamic Games}, | |
| editor = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {7}, | |
| year = {2004}, | |
| pages = {196--200}, | |
| abstract = {The many-player game of selling an asset, introduced by Sakaguchi and extended to monotone voting procedures by Yasuda, Nakagami and Kurano, is reviewed. Conditions for a unique equilibrium among stationary threshold strategies are given.} | |
| } | |
| @Techreport{Ferguson:2008, | |
| author = {Ferguson, Thomas S.}, | |
| title = {The Sum-the-Odds Theorem with Application to a Stopping Game of {S}akaguchi}, | |
| institution = {http:// www.math.ucla.edu/~tom}, | |
| year = {2008}, | |
| abstract = {The optimal stopping problem of maximizing the probability of stop- ping on the last success of a finite sequence of independent Bernoulli trials has been studied by Hill and Krengel (1992), Hsiau and Yang (2000) and Bruss (2000). The optimal stopping rule of Bruss stops when the sum of the odds of future successes is less than one. This Sum-the-Odds Theorem is extended in several ways. First, an infinite number of Bernoulli trials is allowed. Second, the payoff for not stopping is allowed to be different from the payoff of stopping on a success that is not the last success. Third, the Bernoulli variables are allowed to be dependent. Fourth, the model is generalized to allow at each stage other dependent random variables to be observed that may influence the assessment of the probability of success at future stages. Finally, application is made to a game of Sakaguchi (1984) in which two players vie for predicting the last success, but in which one of the players is given priority of acting first.} | |
| } | |
| @Article{Flatau:Irle:1983, | |
| author = {Flatau, J. and Irle, A.}, | |
| title = {Optimal Stopping for Extremal Processes}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {16}, | |
| number = {}, | |
| year = {1983}, | |
| pages = {99-111} | |
| } | |
| @Article{Frank:Samuels:1980, | |
| author = {Frank, Arthur Q. and Samuels, Stephen M.}, | |
| title = {On an Optimal Stopping Problem of {G}usein-{Z}ade}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {10}, | |
| number = {3}, | |
| year = {1980}, | |
| pages = {299--311}, | |
| abstract = {We study the problem of selecting one of the r best of n rankable individuals arriving in random order, in which selection must be made with a stopping rule based only on the relative ranks of the successive arrivals.[...]} | |
| } | |
| @Article{Freeman:1983, | |
| author = {Freeman, P.R.}, | |
| title = {The Secretary Problem and its Extensions: A Review}, | |
| journal = {International Statistical Review}, | |
| volume = {13}, | |
| number = {}, | |
| year = {1983}, | |
| pages = {189-206} | |
| } | |
| @Article{Frid:1968, | |
| author = {Frid, E. B.}, | |
| title = {The Optimal Stopping Rule for a Two-Person {M}arkov Chain with Opposing Interests}, | |
| journal = {Theory of Probability and Its Applications}, | |
| volume = {14}, | |
| number = {4}, | |
| year = {1968}, | |
| pages = {713-716} | |
| } | |
| @Article{Fushimi:1981, | |
| author = {Fushimi, Masanori}, | |
| title = {The Secretary Problem in a Competitive Situation}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {24}, | |
| number = {4}, | |
| year = {1981}, | |
| month = {December}, | |
| pages = {350-358} | |
| } | |
| @Article{Gaver:1976, | |
| author = {Gaver, Donald P.}, | |
| title = {Random Record Models}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {13}, | |
| number = {3}, | |
| year = {1976}, | |
| month = {September}, | |
| pages = {538--547} | |
| } | |
| @Article{Gianini:1977, | |
| author = {Gianini, Jacqueline}, | |
| title = {The Infinite Secretary Problem as the Limit of the Finite Problem}, | |
| journal = {Annals of Probability}, | |
| volume = {5}, | |
| number = {4}, | |
| year = {1977}, | |
| pages = {636-644} | |
| } | |
| @Article{Gianini:Samuels:1976, | |
| author = {Gianini, Jacqueline and Samuels, Stephen M.}, | |
| title = {The Infinite Secretary Problem}, | |
| journal = {Annals of Probability}, | |
| volume = {4}, | |
| number = {3}, | |
| year = {1976}, | |
| pages = {418-432} | |
| } | |
| @Article{Gilbert:Mosteller:1966, | |
| author = {Gilbert, John P. and Mosteller, Frederick}, | |
| title = {Recognizing the Maximum of a Sequence}, | |
| journal = {Annals of Probability}, | |
| volume = {61}, | |
| number = {313}, | |
| year = {1966}, | |
| month = {March}, | |
| pages = {35-73} | |
| } | |
| @Article{Glasser:Barron:1983, | |
| author = {Glasser, Kenneth S. and Barron, Richard Holzsager Austin}, | |
| title = {The d choice secretary problem}, | |
| journal = {Communications in Statistics. Part C: Sequential Analysis}, | |
| volume = {2}, | |
| number = {3}, | |
| year = {1983}, | |
| pages = {177-199}, | |
| abstract = {In the classical Secretary Problem, the player tries to choose the best object of a sequentially ordered set of size $N$. The value of each object is given by its rank only. At any stage, the player knows the rank of the current object relative to those already seen. Once rejected, an object cannot be chosen later. In this paper, a generalized Secretary Problem is discussed. The player is given d choices to choose all of the d best objects. The optimal procedure is found by converting the d choice Secretary Problem into a ``walk'' in a two-dimensional grid. A simple approximation to the optimal strategy rule is also presented.} | |
| } | |
| @Article{Glickman:2000, | |
| author = {Glickman, Hagit}, | |
| title = {A Best Choice Problem with Multiple Selectors}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {37}, | |
| number = {}, | |
| year = {2000}, | |
| pages = {718-735} | |
| } | |
| @Article{Gnedin:1994, | |
| author = {Gnedin, Alexander V.}, | |
| title = {A Solution to the Game of {G}oogol}, | |
| journal = {The Annals of Probability}, | |
| volume = {22}, | |
| number = {3}, | |
| year = {1994}, | |
| pages = {1588-1595} | |
| } | |
| @Article{Gnedin:2004, | |
| author = {Gnedin, Alexander V.}, | |
| title = {Best Choice from the Planar Poisson Process}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {111}, | |
| number = {2}, | |
| year = {2004}, | |
| pages = {317-354}, | |
| abstract = {Various best-choice problems related to the planar homogeneous Poisson process in a finite or semi-infinite rectangle are studied. The analysis is largely based on the properties of the one-dimensional box-area process associated with the sequence of records. We prove a series of distributional identities involving exponential and uniform random variables, and give a resolution to the Petruccelli–Porosinski–Samuels paradox on the coincidence of asymptotic values in certain discrete-time optimal stopping problems.} | |
| } | |
| @Incollection{Gnedin:2000, | |
| author = {Gnedin, Alexander V.}, | |
| title = {Sequential Selection of an Increasing Subsequence from a Random Sample with Geometrically Distributed Sample Size}, | |
| booktitle = {Game Theory, Optimal Stopping, Probability and Statistics}, | |
| editor = {Bruss, F. Thomas and Le Cam, Lucien}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Lecture Notes--Monograph Series}, | |
| volume = {35}, | |
| number = {}, | |
| year = {2000}, | |
| month = {}, | |
| pages = {101--109} | |
| } | |
| @Article{Gnedin:Krengel:1995, | |
| author = {Gnedin, Alexander V. and Krengel, Ulrich}, | |
| title = {A Stochastic Game of Optimal Stopping and Order Selection}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {5}, | |
| number = {1}, | |
| year = {1995}, | |
| pages = {310-321} | |
| } | |
| @Article{Gnedin:Krengel:1996, | |
| author = {Gnedin, Alexander V. and Krengel, Ulrich}, | |
| title = {Optimal Selection Problems Based On Exchangeable Trials}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {6}, | |
| number = {3}, | |
| year = {1996}, | |
| pages = {862-882} | |
| } | |
| @Article{Gnedin:Sakaguchi:1992, | |
| author = {Gnedin, Alexander V.}, | |
| title = {On a Best Choice Problem Related to the Poisson Process}, | |
| journal = {Contemporary Mathematics}, | |
| publisher = {American Mathematical Society}, | |
| volume = {125}, | |
| year = {1992}, | |
| pages = {59-64}, | |
| abstract = {We consider a full information best choice problem with Poisson arrivals. We find the optimal stopping rule and represent its value as an analytical function of the expected number of arrivals.} | |
| } | |
| @Article{Goel:Rubin:1996, | |
| author = {Goel, Prem K. and Rubin, Herman}, | |
| title = {On Selecting a Subset Containing the Best Population-A Bayesian Approach}, | |
| journal = {The Annals of Statistics}, | |
| volume = {5}, | |
| number = {5}, | |
| year = {1977}, | |
| month = {September}, | |
| pages = {969-983} | |
| } | |
| @Article{Goldie:Rogers:1984, | |
| author = {Goldie, Charles M. and Rogers, L.C.G.}, | |
| title = {The k-Record Processes are i.i.d.}, | |
| journal = {Probability Theory and Related Fields}, | |
| volume = {67}, | |
| number = {2}, | |
| year = {1984}, | |
| pages = {197-211} | |
| } | |
| @Article{Goldie:Resnick:1995, | |
| author = {Goldie, Charles M. and Resnick, Sidney I.}, | |
| title = {Many Multivariate Records}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {59}, | |
| number = {2}, | |
| year = {1995}, | |
| pages = {185-216}, | |
| abstract = {(Xn)n=1,2,… is a sequence of independent, identically distributed random vectors in R2. Say Xn is a record if there is a record simultaneously in both coordinates at index n. The total number of records of a sequence is frequently finite so we consider the behaviour of the records in a fixed rectangle A conditional on there being a large number of records \{NA\} in the rectangle. We join the records up to form a random parametrized curve, and prove that, under suitable conditions, as the number of records in the rectangle goes to infinity the random curves converge conditionally in probability to a non-random limit parametrized curve, which we characterize. We also prove a large-deviation result for the random curves. } | |
| } | |
| @Article{Goldstein:Samuel-Cahn:2006, | |
| author = {Goldstein, Larry and Samuel-Cahn, Ester}, | |
| title = {Optimal Two-Choice Stopping on an Exponential Sequence}, | |
| journal = {Sequential Analysis}, | |
| volume = {25}, | |
| number = {}, | |
| year = {2006}, | |
| pages = {351-363} | |
| } | |
| @Article{Grun:2013, | |
| author = {Grun, Christine}, | |
| title = {On {D}ynkin Games with Incomplete Information}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {51}, | |
| number = {5}, | |
| year = {2013}, | |
| pages = {4039-4065} | |
| } | |
| @Article{Gusein-Sade:1967, | |
| author = {Gusein-Sade, S. M.}, | |
| title = {The Problem of Choice and the Optimal Stopping Rule for a Sequence of Independent Trials}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {11}, | |
| number = {}, | |
| year = {1967}, | |
| pages = {472-476} | |
| } | |
| @Article{Haggstrom:1967, | |
| author = {Haggstrom, Gus W.}, | |
| title = {Optimal Sequential Procedures When More than One Stop is Required}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| volume = {38}, | |
| number = {6}, | |
| year = {1967}, | |
| month = {June}, | |
| pages = {1618--1626} | |
| } | |
| @Article{Hamadene:2006, | |
| author = {S. Hamadene}, | |
| title = {Mixed Zero-Sum Stochastic Differential Game and American Game Options}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {45}, | |
| number = {2}, | |
| pages = {496-518}, | |
| year = {2006} | |
| } | |
| @Article{Hamadene:Zhang:2010, | |
| author = {Said Hamadene and Jianfeng Zhang}, | |
| title = {The Continuous Time Nonzero-Sum {D}ynkin Game Problem and Application in Game Options}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {48}, | |
| number = {5}, | |
| pages = {3659-3669}, | |
| year = {2010} | |
| } | |
| @Article{Hamadene:Hassani:2014a, | |
| author = {Hamadene, Said and Hassani, Mohammed}, | |
| title = {The Multiplayer Nonzero-Sum {D}ynkin Game in Discrete Time}, | |
| journal = {Mathematical Methods of Operations Research}, | |
| volume = {79}, | |
| pages = {179-194}, | |
| year = {2014} | |
| } | |
| @Article{Hamadene:Hassani:2014b, | |
| author = {Hamadene, Said and Hassani, Mohammed}, | |
| title = {The Multiplayer Nonzero-Sum {D}ynkin Game in Continuous Time}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {52}, | |
| number = {2}, | |
| pages = {821-835}, | |
| year = {2014} | |
| } | |
| @Article{Hill:Kennedy:1992, | |
| author = {Hill, Theodore P. and Kennedy, D. P.}, | |
| title = {Sharp Inequalities for Optimal Stopping with Rewards Based on Ranks}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {2}, | |
| number = {2}, | |
| year = {1992}, | |
| pages = {503-517}, | |
| abstract = {A universal bound for the maximal expected reward is obtained for stopping a sequence of independent random variables where the reward is a nonincreasing function of the rank of the variable selected. This bound is shown to be sharp in three classical cases: (i) when maximizing the probability of choosing one of the k best; (ii) when minimizing the expected rank; and (iii) for an exponential function of the rank.} | |
| } | |
| @Article{Hill:Kennedy:1994, | |
| author = {Hill, Theodore P. and Kennedy, D. P.}, | |
| title = {Minimax-Optimal Strategies for the Best-Choice Problem When a Bound is Known for the Expected Number of Objects}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {32}, | |
| number = {4}, | |
| year = {1994}, | |
| pages = {937-951}, | |
| abstract = {For the best-choice (or secretary) problem wiith an unknown number $N$ of objects, minimax-optimal strategies for the observer and minimax distributions for $N$ are derived under the assumption that $N$ is a random variable with expected value at most $M$, where $M$ is known. The solution is derived as a special case of the situation where $N$ is constrained by $Ef(N) \leq M$, where $f$ is increasing with $f(i)-f(i-1)$ convex.} | |
| } | |
| @Article{Hill:Kertz:1982, | |
| author = {Hill, Theodore P. and Kertz, Robert P.},}, | |
| title = {Comparison of Stop Rules and Supremum Expectations of I.I.D. Random Variables}, | |
| journal = {The Annals of Probability}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {10}, | |
| number = {2}, | |
| year = {1982}, | |
| pages = {336-345} | |
| } | |
| @Article{Hill:Kertz:1992, | |
| author = {Hill, Theodore P. and Kertz, Robert P.},}, | |
| title = {A Survey of Prophet Inequalities in Optimal Stopping Theory}, | |
| journal = {Contemporary Mathematics}, | |
| publisher = {American Mathematical Society}, | |
| volume = {125}, | |
| year = {1992}, | |
| pages = {191-207} | |
| } | |
| @Article{Hill:Krengel:1991, | |
| author = {Hill, Theodore P. and Krengel, Ulrich}, | |
| title = {Minimax-Optimal Stop Rules and Distributions in Secretary Problems}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {19}, | |
| number = {1}, | |
| year = {1991}, | |
| pages = {342-353}, | |
| abstract = {For the secretary (or best-choice problem with an unknown number $N$ of objects, minimax-optimal stop rules and (worst-case) distributions are derived, under the assumption that $N$ is a random variable with unknown distribution, but known upper bound $n$. Asymptotically, the probability of selecting the best object in this situation is of order of $(\log n)^{-1}$. For example, even if the only information available is that there are somewhere between $1$ and $100$ objects, there is still a strategy which will select the best item about one time in five.} | |
| } | |
| @Article{Hill:Krengel:1992, | |
| author = {Hill, Theodore P. and Krengel, Ulrich}, | |
| title = {On the Game of Googol}, | |
| journal = {International Journal of Game Theory}, | |
| volume = {21}, | |
| number = {}, | |
| year = {1992}, | |
| pages = {151-160}, | |
| abstract = {In the classical secretary problem the decision maker can only observe the relative ranks of the items presented. Recently, Ferguson -- building on ideas of Stewart -- showed that, in a game theoretic sense,'there is no advantage if the actual values of the random variables underlying the relative ranks can be observed (game of googol). We extend this to the case where the number of items is unknown with a known upper bound. Corollary 3 extends one of the main results in [HK] to all randomized stopping times. We also include a modified, somewhat more formal argument for Ferguson's result.} | |
| } | |
| @Article{Hlynka:Sheahan:1988, | |
| author = {Hlynka, M. and Sheahan, J. N.}, | |
| title = {The Secretary Problem for a Random Walk}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {28}, | |
| number = {2}, | |
| year = {1988}, | |
| pages = {317--325}, | |
| abstract = {The secretary problem for a random walk is described. A particle has equal probabilities of moving j steps up or j steps down. The optimal strategy of picking the maximum height in n steps without the opportunity of recall is found. The best strategy is shown to be exactly the same as the naive strategy of choosing the first element of the sequence. The theory is extended to symmetric continuous distributions.} | |
| } | |
| @Article{Hsiau:Yang:2000, | |
| author = {Hsiau, Shoou-Ren and Yang, Jiing-Ru}, | |
| title = {A Natural Variation of the Standard Secretary Problem}, | |
| journal = {Statistica Sinica}, | |
| volume = {10}, | |
| year = {2000}, | |
| pages = {639--646}, | |
| abstract = {We consider a natural variation of the standard secretary problem: $N$ groups of applicants are to be interviewed sequentially (in groups) by a manager and the manager wants to find a strategy which maximizes the probability of selecting the best applicant. We use the usual backward induction method to find the optimal strategy, which can be easily described and is a natural extension of the solution for the standard secretary problem.} | |
| } | |
| @Incollection{Hubert:Pyke:2000, | |
| author = {Hubert, Steven L. and Pyke, Ronald}, | |
| title = {Sequential Estimation of Functions of $p$ for Bernoulli Trials}, | |
| booktitle = {Game Theory, Optimal Stopping, Probability and Statistics}, | |
| editor = {Bruss, F. Thomas and Le Cam, Lucien}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Lecture Notes -- Monograph Series}, | |
| volume = {35}, | |
| year = {2000}, | |
| pages = {263--294} | |
| } | |
| @Incollection{Immorlica:Kleinberg:Mahdian:2006, | |
| author = {Immorlica, Nicole and Kleinberg, Robert and Mahdian, Mohammad}, | |
| title = {Secretary Problems with Competing Employers}, | |
| booktitle = {Internet and Network Economics}, | |
| series = {Lecture Notes in Computer Science}, | |
| volume = {4286}, | |
| editor = {Spirakis, Paul and Mavronicolas, Marios and Kontogiannis, Spyros}, | |
| publisher = {Springer Berlin Heidelberg}, | |
| year = {2006}, | |
| pages = {389--400} | |
| } | |
| @Article{Kadota:KuranoYasuda:2006, | |
| author = {Kadota, Yoshinobu and Kurano, Masami and Yasuda, Masami}, | |
| title = {Discounted {M}arkov Decision Processes with Utility Constraints}, | |
| journal = {Computers and Mathematics with Applications}, | |
| volume = {51}, | |
| number = {2}, | |
| year = {2006}, | |
| pages = {279--284}, | |
| abstract = {We consider utility-constrained Markov decision processes. The expected utility of the total discounted reward is maximized subject to multiple expected utility constraints. By introducing a corresponding Lagrange function, a saddle-point theorem of the utility constrained optimization is derived. The existence of a constrained optimal policy is characterized by optimal action sets specified with a parametric utility.} | |
| } | |
| @Article{Karpowicz:Szajowski:2007a, | |
| author = {Karpowicz, Anna and Szajowski, Krzysztof}, | |
| title = {Double Optimal Stopping Times and Dynamic Pricing Problem: Description of the Mathematical Model}, | |
| journal = {Mathematical Methods of Operations Research}, | |
| volume = {66}, | |
| number = {}, | |
| year = {2007}, | |
| pages = {235--253} | |
| } | |
| @Article{Karpowicz:Szajowski:2007b, | |
| author = {Karpowicz, Anna and Szajowski, Krzysztof}, | |
| title = {Double Optimal Stopping of a Risk Process}, | |
| journal = {Stochastics: An International Journal of Probability and Stochastics Processes}, | |
| volume = {79}, | |
| number = {1--2}, | |
| year = {2007}, | |
| month = {February-April}, | |
| pages = {155--167} | |
| } | |
| @Article{Kawai:Tamaki:2003, | |
| author = {Kawai, M. and Tamaki, M.}, | |
| title = {Choosing Either the Best or the Second Best when the Number of Applicants is Random}, | |
| journal = {Applied Stochastic System Modelling}, | |
| volume = {46}, | |
| number = {7}, | |
| year = {2003}, | |
| pages = {1065--1071}, | |
| abstract = {Gusein-Zade considered a version of the secretary problem in which we are allowed to make one choice and regard the choice as successful when the chosen applicant is either the best or the second best among all N applicants, where N is a given constant. Here we attempt to generalize his problem to the one in which N is a random variable whose distribution is known. The optimality equations are derived for any given distribution of N, but our main concerns are to investigate, in detail, the case where N is uniformly distributed on [1, m]. It can be shown that, in this case, the optimal policy has the form similar to that of the Gusein-Zade problem: pass s1 - 1 applicants, then choose the relatively best applicant thereafter (if any), but beginning with the s2(≥ s1)th stage, choose also the relatively second best applicant (if any). Some asymptotics concerning the critical numbers s1 and s2, and the success probability, are also obtained.} | |
| } | |
| @Article{Kennedy:1986, | |
| author = {Kennedy, Douglas P.}, | |
| title = {Optimal Sequential Assignment}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {11}, | |
| number = {4}, | |
| year = {1986}, | |
| month = {November}, | |
| pages = {619--626}, | |
| abstract = {For each job $n$ ($= 1,..., N$) there is an associated random variable $X_n$ and for each person $m$ ($= 1,...,N$) there is an associated constant $p_{m}$ so that if job $n$ is assigned to person $m$ a reward $p_{m}X_{n}$ is obtained. We do not assume that the $X_n$ are necessarily independent. The jobs are observed sequentially and must be assigned nonanticipatively to the persons so as to maximise the total expected reward. The optimal assignment is established for both the case when $N$ is finite and when $N$ is infinite.} | |
| } | |
| @Article{Kennedy:Kertz:1990, | |
| author = {Kennedy, Douglas P. and Kertz, Robert P.}, | |
| title = {Limit Theorems for Threshold-Stopped Random Variables with Applications to Optimal Stopping}, | |
| journal = {Advances in Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {22}, | |
| number = {2}, | |
| month = {June}, | |
| year = {1990}, | |
| pages = {396--411}, | |
| abstract = {The extremal types theorem identifies asymptotic behaviour for the maxima of sequences of i.i.d. random variables. A parallel theorem is given which identifies the asymptotic behaviour of sequences of threshold-stopped random variables. Three new types of limit distributions arise, but normalizing constants remain the same as in the maxima case. Limiting joint distributions are also given for maxima and threshold-stopped random variables. Applications to the optimal stopping of i.i.d. random variables are given.} | |
| } | |
| @Article{Kennedy:Kertz:1991, | |
| author = {Kennedy, Douglas P. and Kertz, Robert P.}, | |
| title = {The Asymptotic Behavior of the Reward Sequence in the Optimal Stopping of I.I.D. Random Variables}, | |
| journal = {The Annals of Probability}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {19}, | |
| number = {1}, | |
| year = {1991}, | |
| month = {January}, | |
| pages = {pp. 329-341} | |
| } | |
| @Article{Kennedy:Kertz:1992a, | |
| author = {Kennedy, Douglas P. and Kertz, Robert P.}, | |
| title = {Comparison of Optimal Stopping Values and Expected Suprema for i.i.d. r.v.s with Costs and Discounting}, | |
| journal = {Contemporary Mathematics}, | |
| publisher = {American Mathematical Society}, | |
| volume = {125}, | |
| year = {1992}, | |
| pages = {217--230} | |
| } | |
| @Article{Kennedy:Kertz:1992b, | |
| author = {Kennedy, Douglas P. and Kertz, Robert P.}, | |
| title = {Limit Theorems for Suprema, Threshold-Stopped Random Variables and Last Exits of i.i.d. Random Variables with Costs and Discounting, with Applications to Optimal Stopping}, | |
| journal = {Advances in Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {24}, | |
| number = {2}, | |
| year = {1992}, | |
| month = {June}, | |
| pages = {241--266}, | |
| abstract = {For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.} | |
| } | |
| @Article{Kennedy:Kertz:1997, | |
| author = {Kennedy, Douglas P. and Kertz, Robert P.}, | |
| title = {A Prophet Inequality for Independent Random Variables with Finite Variances}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {34}, | |
| year = {1997}, | |
| pages = {945--958} | |
| } | |
| @Article{Kifer:1971, | |
| author = {Kifer, Yuri I.}, | |
| title = {Optimal Stopped Games}, | |
| journal = {Theory of Probability and Its Applications}, | |
| volume = {16}, | |
| number = {1}, | |
| year = {1971}, | |
| pages = {185--189} | |
| } | |
| @Article{Kifer:2000, | |
| author = {Kifer, Yuri I.}, | |
| title = {Game Options}, | |
| journal = {Finance and Stochastics}, | |
| publisher = {Springer-Verlag}, | |
| volume = {4}, | |
| year = {2000}, | |
| pages = {443--463} | |
| } | |
| @Article{Kifer:2006, | |
| author = {Kifer, Yuri I.}, | |
| title = {Error Estimates for Binomial Approximations of Game Options}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {16}, | |
| number = {2}, | |
| year = {2006}, | |
| month = {May}, | |
| pages = {984--1033} | |
| } | |
| @Article{Kifer:2013, | |
| author = {Kifer, Yuri I.}, | |
| title = {{D}ynkin's Games and {I}sraeli Options}, | |
| journal = {International Scholarly Research Network Probability and Statistics}, | |
| year = {2013}, | |
| pages = {1--17} | |
| } | |
| @Article{Krasnosielska:Ferenstein:2013, | |
| author = {Krasnosielska-Kobos, Anna and Ferenstein, Elzbieta}, | |
| title = {Construction of {N}ash Equilibrium in a Game Version of {E}lfving's Multiple Stopping Problem}, | |
| journal = {Dynamic Games and Applications}, | |
| publisher = {SP Birkhauser Verlag Boston}, | |
| volume = {3}, | |
| number = {2}, | |
| year = {2013}, | |
| pages = {220--235} | |
| } | |
| @Article{Krieger:Pollak:SamuelCahn:2007, | |
| author = {Krieger, Abba M. and Pollak, Moshe and Samuel-Cahn, Ester}, | |
| title = {Select Sets: Rank and File}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {17}, | |
| number = {1}, | |
| year = {2007}, | |
| month = {February}, | |
| pages = {360--385} | |
| } | |
| @Article{Krieger:Pollak:SamuelCahn:2010, | |
| author = {Krieger, Abba M. and Pollak, Moshe and Samuel-Cahn, Ester}, | |
| title = {Extreme(ly) Mean(ingful): Sequential Formation of a Quality Group}, | |
| journal = {The Annals of Applied Probability}, | |
| volume = {20}, | |
| number = {6}, | |
| year = {2010}, | |
| month = {December}, | |
| pages = {2261--2294} | |
| } | |
| @Article{Krieger:SamuelCahn:2009, | |
| author = {Krieger, Abba M. and Samuel-Cahn, Ester}, | |
| title = {The Secretary Problem of Minimizing the Expected Rank: a Simple Suboptimal Approach with Generalizations}, | |
| journal = {Advances in Applied Probability}, | |
| volume = {41}, | |
| number = {4}, | |
| year = {2009}, | |
| month = {December}, | |
| pages = {1041--1058} | |
| } | |
| @Article{Krieger:SamuelCahn:2012, | |
| author = {Krieger, Abba M. and Samuel-Cahn, Ester}, | |
| title = {The Noisy Secretary Problem and Some Results on Extreme Concomitant Variables}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {49}, | |
| number = {3}, | |
| year = {2007}, | |
| month = {September}, | |
| pages = {821--837} | |
| } | |
| @Article{Kubicki:Morayne:2005, | |
| author = {Grzegorz Kubicki and Michal Morayne}, | |
| title = {Graph-Theoretic Generalization of the Secretary Problem: The Directed Path Case}, | |
| journal = {{S}{I}{A}{M} Journal on Discrete Mathematics}, | |
| volume = {19}, | |
| number = {3}, | |
| year = {2005}, | |
| pages = {622-632} | |
| } | |
| @Article{Kuchta:Morayne:2014, | |
| author = {Kuchta, Malgorzata and Morayne, Michal}, | |
| title = {A Secretary Problem with Many Lives}, | |
| journal = {Communications in Statistics - Theory and Methods}, | |
| volume = {43}, | |
| number = {1}, | |
| year = {2014}, | |
| pages = {210-218}, | |
| abstract = {We consider a secretary type problem where an administrator who has only one on-line choice in $m$ consecutive searches has to choose the best candidate in one of them.} | |
| } | |
| @Article{Kuhne:Ruschendorf:2000a, | |
| author = {Kuhne, Robert and Ruschendorf, Ludger}, | |
| title = {Approximation of Optimal Stopping Problems}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {90}, | |
| number = {2}, | |
| year = {2000}, | |
| month = {September}, | |
| pages = {301-325}, | |
| abstract = {We consider optimal stopping of independent sequences. Assuming that the corresponding imbedded planar point processes converge to a Poisson process we introduce some additional conditions which allow to approximate the optimal stopping problem of the discrete time sequence by the optimal stopping of the limiting Poisson process. The optimal stopping of the involved Poisson processes is reduced to a differential equation for the critical curve which can be solved in several examples. We apply this method to obtain approximations for the stopping of iid sequences in the domain of max-stable laws with observation costs and with discount factors.} | |
| } | |
| @Article{Kuhne:Ruschendorf:2000b, | |
| author = {Kuhne, Robert and Ruschendorf, Ludger}, | |
| title = {Optimal Stopping with Discount and Observation Costs}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {37}, | |
| number = {1}, | |
| year = {2000} | |
| month = {03}, | |
| pages = {64--72}, | |
| abstract = {For i.i.d. random variables in the domain of attraction of a max-stable distribution with discount and observation costs we determine asymptotic approximations of the optimal stopping values and asymptotically optimal stopping times. The results are based on Poisson approximation of related embedded planar point processes. The optimal stopping problem for the limiting Poisson point processes can be reduced to differential equations for the boundaries. In several cases we obtain numerical solutions of the differential equations. In some cases the analysis allows us to obtain explicit optimal stopping values. This approach thus leads to approximate solutions of the optimal stopping problem of discrete time sequences.} | |
| } | |
| @Article{Kurano:Nakagami:Yasuda:1980, | |
| author = {Kurano, Masami and Nakagami, J. and Yasuda, Masami}, | |
| title = {Multi-Variate Stopping Problem with a Majority Rule}, | |
| journal = {Journal of Operations Research of the Society of {J}apan}, | |
| volume = {23}, | |
| number = {3}, | |
| year = {1980}, | |
| month = {September}, | |
| pages = {205--222} | |
| } | |
| @Techreport{Laraki:Solan:2012, | |
| author = {Laraki, Rida and Solan, Eilon} | |
| title = {Equilibrium in Two-Player Nonzero-Sum {D}ynkin Games in Continuous Time}, | |
| institution = {Cahier de Recherche, Departement d'Economie, Ecole Polytechnique}, | |
| volume = {25}, | |
| year = {2012} | |
| } | |
| @Article{Lehtinen:1997, | |
| author = {Lehtinen, Aarni}, | |
| title = {Optimal Selection of the $k$ Best of a Sequence with $k$ Stops}, | |
| journal = {Mathematical Methods of Operations Research}, | |
| publisher = {Physica-Verlag}, | |
| volume = {46}, | |
| number = {2}, | |
| year = {1997}, | |
| pages = {251--261} | |
| } | |
| @Article{Lehtinen:1993a, | |
| author = {Lehtinen, Aarni}, | |
| title = {The Best Choice Problem with an Unknown Number of Objects}, | |
| journal = {Zeitschrift fur Operations Research}, | |
| publisher = {Physica-Verlag}, | |
| volume = {37}, | |
| number = {1}, | |
| year = {1993}, | |
| pages = {97--106} | |
| } | |
| @Article{Lehtinen:1993b, | |
| author = {Lehtinen, Aarni}, | |
| title = {Optimal Selection of the Four Best of a Sequence}, | |
| journal = {Zeitschrift fur Operations Research}, | |
| publisher = {Physica-Verlag}, | |
| volume = {38}, | |
| number = {3}, | |
| year = {1993}, | |
| pages = {309--315} | |
| } | |
| @Techreport{Lim:Bearden:Smith:date, | |
| author = {Lim, Churlzu and Bearden, J. Neil and Smith, J. Cole}, | |
| title = {Sequential Search with Multi-Attribute Options}, | |
| institution = {Preprint DECISION ANALYSIS}, | |
| publisher = {INFORMS}, | |
| volume = {}, | |
| number = {}, | |
| year = {}, | |
| pages = {}, | |
| abstract = {We describe a search problem in which a decision maker (DM) must select several sequentially-encountered options. Each option is described by multiple attributes, and the value of an option is given by a function of its attribute values. However, the attribute values are not known with certainty, and can only be ascertained in a predefined order, at some fixed cost. During the search the DM can choose to select an option, purchase information about an attribute value, reject (permanently) the current option and continue the search, or terminate the search and accept a status quo outcome. We introduce a Threshold Policy for this search process, and provide a class of option value functions for which the policy is optimal. We then furnish a dynamic programming procedure for prescribing an optimal policy for this problem. Finally, we derive analytic solutions to some special cases of the problem, and present a case study that demonstrates a possible use of the proposed approach.} | |
| } | |
| @Article{Lindley:1961, | |
| author = {Lindley, D. V.}, | |
| title = {Dynamic Programming and Decision Theory}, | |
| journal = {Journal of the Royal Statistical Society}, | |
| series = {Series C (Applied Statistics)}, | |
| volume = {10}, | |
| number = {1}, | |
| year = {1961}, | |
| month = {March}, | |
| pages = {39--51} | |
| } | |
| @Article{Loertscher:Muehlheusser:2011, | |
| author = {Loertscher, Simon and Muehlheusser, Gerd}, | |
| title = {Sequential Location Games}, | |
| journal = {The RAND Journal of Economics}, | |
| publisher = {Blackwell Publishing Inc}, | |
| volume = {42}, | |
| number = {4}, | |
| year = {2011}, | |
| pages = {639--663}, | |
| abstract = {We study location games where market entry is costly and occurs sequentially, and where consumers are nonuniformly distributed over the unit interval. We show that for certain classes of densities, including monotone and—under some additional restrictions—hump-shaped and U-shaped ones, equilibrium locations can be determined independently of when they are occupied. Our analysis reveals a number of peculiarities of the uniform distribution. Extensions of the model allow for price competition and advertisement in media markets, winner-take-all competition, trade-offs between profits in the short and the long run, and firms operating multiple outlets.} | |
| } | |
| @Article{Lorenzen:1979, | |
| author = {Lorenzen, T. J.}, | |
| title = {Generalizing the Secretary Problem}, | |
| journal = {Advances in Applied Probability}, | |
| volume = {11}, | |
| number = {}, | |
| year = {1979}, | |
| month = {}, | |
| pages = {384-396} | |
| } | |
| @Article{Lorenzen:1981, | |
| author = {Lorenzen, T. J.}, | |
| title = {Optimal Stopping with Sampling Cost: The Secretary Problem}, | |
| journal = {Annals of Probability}, | |
| volume = {9}, | |
| number = {1}, | |
| year = {1981}, | |
| pages = {167-172} | |
| } | |
| @Article{Ludkovski:2009, | |
| author = {Ludkovski, Michael}, | |
| title = {A Simulation Approach to Optimal Stopping Under Partial Information}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {119}, | |
| number = {12}, | |
| pages = {4061-4087}, | |
| year = {2009}, | |
| abstract = {We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional diffusion with correlated noise. Such models where the controller is not fully aware of her environment are of interest in applied probability and financial mathematics. We propose a new approximate numerical algorithm based on the particle filtering and regression Monte Carlo methods. The algorithm maintains a continuous state space and yields an integrated approach to the filtering and control sub-problems. Our approach is entirely simulation-based and therefore allows for a robust implementation with respect to model specification. We carry out the error analysis of our scheme and illustrate with several computational examples. An extension to discretely observed stochastic volatility models is also considered.} | |
| } | |
| @Article{Ludkovski:2011, | |
| author = {Ludkovski, Michael}, | |
| title = {Stochastic Switching Games and Duopolistic Competition in Emissions Markets}, | |
| journal = {{S}{I}{A}{M} Journal on Financial Mathematics}, | |
| volume = {2}, | |
| number = {1}, | |
| pages = {488-511}, | |
| year = {2011}, | |
| abstract = { | |
| We study optimal behavior of energy producers under a CO2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reduced-form price-impact model for the CO2 allowance price. Such duopolistic competition results in a new type of a non-zero-sum stochastic switching game on finite horizon. Existence of game Nash equilibria is established through generalization to randomized switching strategies. No uniqueness is possible and we therefore consider a variety of correlated equilibrium mechanisms. We prove existence of correlated equilibrium points in switching games and give a recursive description of equilibrium game values. A simulation-based algorithm to solve for the game values is constructed and a numerical example is presented. | |
| } | |
| } | |
| @Article{MacQueen:Miller:1960, | |
| author = {MacQueen, J. and Miller, R. P.}, | |
| title = {Optimal Persistence Policies}, | |
| journal = {Operations Research}, | |
| volume = {8}, | |
| number = {}, | |
| year = {1960}, | |
| pages = {362-380} | |
| } | |
| @Incollection{Mahdian:McAfee:Pennock:2008, | |
| author = {Mahdian, Mohammad and McAfee, Randolph Preston and Pennock, David}, | |
| title = {The Secretary Problem with a Hazard Rate Condition}, | |
| booktitle = {Internet and Network Economics}, | |
| publisher = {Springer Berlin Heidelberg}, | |
| series = {Lecture Notes in Computer Science}, | |
| editor = {Papadimitriou, Christos and Zhang, Shuzhong}, | |
| volume = {5385}, | |
| year = {2008}, | |
| pages = {708-715} | |
| } | |
| @Article{Maitra:Sudderth:1993, | |
| author = {Maitra, A. and Sudderth, W.}, | |
| title = {Borel Stochastic Games with Lim Sup Payoff}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {21}, | |
| number = {2}, | |
| year = {1993}, | |
| month = {April}, | |
| pages = {861--885} | |
| } | |
| @Article{Maitra:Sudderth:2000, | |
| author = {Maitra, A. and Sudderth, W.}, | |
| title = {Randomized Strategies and Terminal Distributions}, | |
| journal = {Lecture Notes-Monograph Series}, | |
| series = {Game Theory, Optimal Stopping, Probability and Statistics}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {35}, | |
| year = {2000}, | |
| pages = {39--52} | |
| } | |
| @Article{Majumdar:1985a, | |
| author = {Majumdar, A. A. K.}, | |
| title = {Optimal Stopping for a Two-Person Sequential Game in the Discrete Case}, | |
| journal = {Pure and Applied Mathematika Sciences}, | |
| volume = {22}, | |
| year = {1985}, | |
| pages = {67-75} | |
| } | |
| @Article{Majumdar:1985b, | |
| author = {Majumdar, A. A. K.}, | |
| title = {Optimal Stopping for a Two-Person Sequential Game in the Continuous Case}, | |
| journal = {Pure and Applied Mathematika Sciences}, | |
| volume = {22}, | |
| year = {1985}, | |
| pages = {79-89} | |
| } | |
| @Article{Mallows:Nair:Shepp:Vardi:1985, | |
| author = {Mallows, C. L. and Nair, V. N. and Shepp, L. A. and Vardi, Y.}, | |
| title = {Optimal Sequential Selection of Secretaries}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {10}, | |
| number = {4}, | |
| year = {1985}, | |
| pages = {709-715} | |
| } | |
| @Article{Mashiah-Yaakovi:2014, | |
| author = {Mashiah-Yaakovi, Ayala}, | |
| title = {Subgame Perfect Equilibria in Stopping Games}, | |
| journal = {International Journal of Game Theory}, | |
| publisher = {Springer Berlin Heidelberg}, | |
| volume = {43}, | |
| number = {1}, | |
| year = {2014}, | |
| pages = {89--135} | |
| } | |
| @Article{Matsui:Ano:2014, | |
| author = {Matsui, Tomomi and Ano, Katsunori}, | |
| title = {A note on a lower bound for the multiplicative odds theorem of optimal stopping}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {51}, | |
| number = {3}, | |
| year = {2014}, | |
| month = {September}, | |
| pages = {885--889} | |
| } | |
| @Article{Mazalov:Falko:2008, | |
| author = {Mazalov, Vladimir and Falko, Anna}, | |
| title = {{N}ash Equilibrium in Two-Sided Mate Choice Problem}, | |
| journal = {International Game Theory Review}, | |
| volume = {10}, | |
| number = {4}, | |
| year = {2008}, | |
| pages = {421-435} | |
| } | |
| @Article{Mazalov:Konovalchikova:2015, | |
| author = {Mazalov, Vladimir and Konovalchikova, Elena}, | |
| title = {The Job-search Problem with Incomplete Information}, | |
| journal = {Procedia Computer Science}, | |
| volume = {55}, | |
| year = {2015}, | |
| pages = {159-164}, | |
| abstract = {This paper considers a best-choice game with incomplete information associated with the job search problem. Players (experts) observe a sequence of independent identically distributed random variables $(x_i, y_i)$, $i = 1, ..., n$, which represent the quality of incoming objects. The first component is announced to the players and the other one is hidden. The players choose an object based on known information about it. The winner is the player having a higher sum of the quality components (total quality) than the opponent. And finally, the optimal strategies of the players are derived.} | |
| } | |
| @Article{Mazalov:Kochetov:1996, | |
| author = {Mazalov, Vladimir and Kochetov, E. A.}, | |
| title = {A Game with Optimal Stopping of Random Walks}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {42}, | |
| number = {4}, | |
| year = {1996}, | |
| pages = {697-702} | |
| } | |
| @Article{Mazalov:Nosalskaya:Tokareva:2014, | |
| author = {Mazalov, Vladimir and Nosalskaya, Tatyana E. and Tokareva, Julia S.}, | |
| title = {Stochastic Cake Division Protocol}, | |
| journal = {International Game Theory Review}, | |
| volume = {16}, | |
| number = {2}, | |
| year = {2014}, | |
| pages = {1-14}, | |
| abstract = {We present a multistage stochastic procedure that produces a fair allocation of a cake among n-person. In each step players observe the collection of the random offers $(x_1,...,x_n)$, where $x_1 + ... + x_n = 1$. As the proposal emerged players have to make a decision to accept it or reject it. The final decision is defined by majority rule or by consensus. The optimal behavior of the players is derived as a class of threshold strategies.} | |
| } | |
| @Article{Mazalov:Sakaguchi:2003, | |
| author = {Mazalov, Vladimir and Sakaguchi, Minoru}, | |
| title = {Location Game on the Plane}, | |
| journal = {International Game Theory Review}, | |
| volume = {5}, | |
| number = {1}, | |
| year = {2003}, | |
| pages = {13-25} | |
| } | |
| @Article{Mazalov:Tamaki:2006, | |
| author = {Mazalov, Vladimir V. and Tamaki, Mitsushi}, | |
| title = {An Explicit Formula for the Optimal Gain in the Full-Information Problem of Owning a Relatively Best Object}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {43}, | |
| number = {1}, | |
| year = {2006} | |
| month = {March}, | |
| pages = {87--101} | |
| } | |
| @Article{McCardle:1985, | |
| author = {McCardle, Kevin F.}, | |
| title = {Information Acquisition and the Adoption of New Technology}, | |
| journal = {Management Science}, | |
| volume = {31}, | |
| number = {11}, | |
| year = {1985}, | |
| month = {November}, | |
| pages = {1372-1389}, | |
| abstract = {The profitability of a new technology is rarely known with certainty at its announcement date. Consequently, prior to making an adoption decision it behooves the firm considering the adoption of this innovation to reduce the level of uncertainty associated with its profitability. The firm accomplishes this by sequentially gathering information, updating its prior estimate of profitability in a Bayesian manner. Quantifying the uncertainty regarding the innovation permits application of dynamic programming techniques: criteria are derived which tell the firm when to stop collecting information and make the adoption decision. It will be shown that it is optimal for the firm to continue to collect information until its estimate of profitability crosses one of two thresholds: upon crossing the upper threshold the firm adopts the technology, whereas the firm rejects the technology if the lower threshold is crossed. The model predicts that even the manager who behaves optimally will occasionally adopt unprofitable technologies and reject profitable ones.} | |
| } | |
| @Article{Morayne:1998, | |
| author = {Morayne, Michal}, | |
| title = {Partial-Order Analogue of the Secretary Problem the Binary Tree Case}, | |
| journal = {Discrete Mathematics}, | |
| volume = {184}, | |
| number = {1-3}, | |
| year = {1982}, | |
| pages = {165-181}, | |
| abstract = {We find an optimal stopping time for the partial-order analogue of the secretary problem in the case of the full binary tree of finite length.} | |
| } | |
| @Article{Mori:1982a, | |
| author = {Mori, Tamas F.}, | |
| title = {On Favourable Stochastic Games}, | |
| journal = {Annales Université Sciences Budapest: Sect. Comput.}, | |
| volume = {3}, | |
| number = {}, | |
| year = {1982}, | |
| pages = {99-101} | |
| } | |
| @Incollection{Mori:1982b, | |
| author = {Mori, Tamas F.}, | |
| title = {How To Win If You Can?}, | |
| booktitle = {Limit Theorems in Probability and Statistics}, | |
| editor = {P. Revesz et al}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Colloq. Math. Soc. J. Bolyai}, | |
| year = {1982}, | |
| pages = {791--806} | |
| } | |
| @Article{Mori:1984, | |
| author = {Mori, Tamas F.}, | |
| title = {The Random Secretary Problem with Multiple Choice}, | |
| journal = {Annales Université Sciences Budapest: Sect. Comput.}, | |
| volume = {5}, | |
| year = {1984}, | |
| pages = {91-102} | |
| } | |
| @Article{Moriguti:1993a, | |
| author = {Moriguti, Sigeiti}, | |
| title = {Basic Theory of Selection By Relative Rank With Cost}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {36}, | |
| number = {1}, | |
| year = {1993}, | |
| pages = {46-61} | |
| } | |
| @Article{Moriguti:1993b, | |
| author = {Moriguti, Sigeiti}, | |
| title = {Asymptotic Theory of Selection By Relative Rank With Medium Cost}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {36}, | |
| number = {2}, | |
| year = {1993}, | |
| pages = {102-117} | |
| } | |
| @Article{Mucci:1973a, | |
| author = {Mucci, Anthony G.}, | |
| title = {On a Class of Secretary Problems}, | |
| journal = {The Annals of Probability}, | |
| volume = {1}, | |
| number = {3}, | |
| year = {1973}, | |
| month = {June}, | |
| pages = {417-427} | |
| } | |
| @Article{Mucci:1973b, | |
| author = {Mucci, Anthony G.}, | |
| title = {Differential Equations and Optimal Choice Problems}, | |
| journal = {The Annals of Statistics}, | |
| volume = {1}, | |
| number = {1}, | |
| year = {1973}, | |
| pages = {104-113} | |
| } | |
| @Article{Nakagami:1999, | |
| author = {Nakagami, J.-I.}, | |
| title = {A Two-Person Non-Cooperative Game for Asset Selling Problem: Independent Case}, | |
| journal = {Computers and Mathematics with Applications}, | |
| publisher = {Elsevier Sciences Ltd}, | |
| volume = {37}, | |
| number = {}, | |
| year = {1999}, | |
| pages = {207--212} | |
| } | |
| @Article{Nakai:1985, | |
| author = {Nakai, Toru}, | |
| title = {The Problem of Optimal Stopping in a Partially Observable {M}arkov Chain}, | |
| journal = {Journal of Optimization Theory and Applications}, | |
| volume = {45}, | |
| number = {3}, | |
| year = {1985}, | |
| month = {March}, | |
| pages = {425-442} | |
| } | |
| @Article{Nakai:1986a, | |
| author = {Nakai, Toru}, | |
| title = {An Optimal Selection Problem for a Sequence with a Random Number of Applicants per Period}, | |
| journal = {Operations Research}, | |
| publisher = {INFORMS}, | |
| volume = {34}, | |
| number = {3}, | |
| year = {1986}, | |
| month = {May-June}, | |
| pages = {478-485} | |
| } | |
| @Article{Nakai:1986b, | |
| author = {Nakai, Toru}, | |
| title = {A Sequential Stochastic Assignment Problem in a Partially Observable Markov Chain}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {11}, | |
| number = {2}, | |
| year = {1986}, | |
| month = {May}, | |
| pages = {230-240} | |
| } | |
| @Article{Nakai:1995, | |
| author = {Nakai, Toru}, | |
| title = {A Partially Observable Decision Problem Under a Shifted Likelihood Ratio Ordering}, | |
| journal = {Mathematical and Computer Modelling}, | |
| volume = {22}, | |
| number = {10-12}, | |
| year = {1995}, | |
| pages = {237-246}, | |
| abstract = {In this paper, we discuss a partially observable sequential decision problem under a shifted likelihood ratio ordering. Since we employ the Bayes' theorem for the learning procedure, we treat this problem under several assumptions. Under these assumptions, we obtain some fundamental results about the relation between prior and posterior information. We also consider an optimal stopping problem for this partially observable Markov decision process.} | |
| } | |
| @Article{Nakai:2006, | |
| author = {Nakai, Toru}, | |
| title = {Properties of a Job Search Problem on a Partially Observable {M}arkov Chain in a Dynamic Economy}, | |
| journal = {Computers and Mathematics with Applications}, | |
| volume = {51}, | |
| number = {2}, | |
| year = {2006}, | |
| pages = {189-198}, | |
| abstract = {This paper observes a job search problem on a partially observable Markov chain, which can be considered as an extension of a job search in a dynamic economy in [1]. This problem is formulated as the state changes according to a partially observable Markov chain, i.e., the current state cannot be observed but there exists some information regarding what a present state is. All information about the unobservable state are summarized by the probability distributions on the state space, and we employ the Bayes' theorem as a learning procedure. The total positivity of order two, or simply TP2, is a fundamental property to investigate sequential decision problems, and it also plays an important role in the Bayesian learning procedure for a partially observable Markov process. By using this property, we consider some relationships among prior and posterior information, and the optimal policy. We will also observe the probabilities to make a transition into each state after some additional transitions by empolying the optimal policy. In the stock market, suppose that the states correspond to the business situation of one company and if there is a state designating the default, then the problem is what time the stocks are sold off before bankrupt, and the probability to become bankrupt will be also observed.} | |
| } | |
| @Incollection{Neumann:Porosinski:Szajowski:1994, | |
| author = {Neumann, Peter and Porosinski, Zdzislaw and Szajowski, Krzysztof}, | |
| title = {On Two-Person Full-Information Best Choice Problem with Imperfect Information}, | |
| booktitle = {Operations Research '93}, | |
| editor = {Bachem, Achim and Derigs, Ulrich and Junger, Michael and Schrader, Rainer}, | |
| publisher = {Physica-Verlag HD}, | |
| year = {1994}, | |
| pages = {355-358}, | |
| abstract = {The paper deals with the following zero-sum game version of the full-information best choice problem. Two person observe sequentially a known number of iid random variables from a known continuous distribution with the object of choosing the largest. The random variables cannot be perfectly observed. Each time a random variable is sampled the sampler is informed only whether it is greater than or less than some level specified by him. Players can choose at most one observation. After each sampling players take a decision for acceptance or rejection of the observation. If both want to accept the same observation the priority is given to the specified player, say Player 1. The class of adequate strategies and the suitable gain function for the problem is constructed. It is shown that the game has solution in pure strategies. The numerical examples are given. The random number of observations is also investigated.} | |
| } | |
| @Article{Neumann:Ramsey:Szajowski:2002, | |
| author = {Neumann, Peter and Ramsey, D. and Szajowski, Krzysztof}, | |
| title = {Randomized Stopping Times in {D}ynkin Games}, | |
| journal = {Zeitschrift fur Angewandte Mathematik und Mechanik}, | |
| volume = {11-12}, | |
| year = {2002}, | |
| pages = {811--819} | |
| } | |
| @Article{Nikolaev:1997, | |
| author = {Nikolaev, M. L.}, | |
| title = {On Optimal Multiple Stopping of Markov Sequences}, | |
| journal = {Theory of Probability and Applications}, | |
| volume = {43}, | |
| number = {2}, | |
| year = {1997}, | |
| pages = {298--306} | |
| } | |
| @Article{Nikolaev:Sofronov:2007, | |
| author = {Nikolaev, M. L. and Sofronov, G. Yu.}, | |
| title = {A Multiple Optimal Stopping Rule for Sums of Independent Random Variables}, | |
| journal = {Discrete Mathematics and Applications}, | |
| volume = {17}, | |
| number = {5}, | |
| year = {2007}, | |
| month = {December}, | |
| pages = {463--473} | |
| } | |
| @Incollection{Nowak:Szajowski:1999, | |
| author = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| title = {Non-Zero-Sum Stochastic Games}, | |
| booktitle = {Stochastic and Differential Games}, | |
| editor = {Bardi, M. and Raghavan, T. E. S. and Parthasarathy, T.}, | |
| publisher = {Birkhauser, Boston}, | |
| year = {1999}, | |
| pages = {297-342} | |
| } | |
| @Article{Ohtsubo:1986, | |
| author = {Ohtsubo, Yoshio}, | |
| title = {{N}eveu's Martingale Conditions and Closedness in {D}ynkin Stopping Problem with a Finite Constraint}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {22}, | |
| number = {}, | |
| year = {1986}, | |
| pages = {333-342} | |
| } | |
| @Article{Ohtsubo:1995, | |
| author = {Ohtsubo, Yoshio}, | |
| title = {{P}areto Optimum In A Cooperative {D}ynkin's Stopping Problem}, | |
| journal = {Nihonkai Mathematical Journal}, | |
| volume = {6}, | |
| number = {2}, | |
| year = {1995}, | |
| pages = {135-151} | |
| } | |
| @Article{Olsson:1974, | |
| author = {Olsson, D.M.}, | |
| title = {A Sequential Simplex Program for Solving Minimization Problems}, | |
| journal = {Journal of Quality Technology}, | |
| volume = {6}, | |
| number = {}, | |
| year = {1974}, | |
| pages = {53-57} | |
| } | |
| @Article{Peskir:1998, | |
| author = {Peskir, Goran}, | |
| title = {Optimal Stopping of the Maximum Process: The Maximality Principle}, | |
| journal = {The Annals of Probability}, | |
| volume = {26}, | |
| number = {4}, | |
| year = {1998}, | |
| pages = {1614-1640} | |
| } | |
| @Article{Peskir:2008, | |
| author = {Peskir, Goran}, | |
| title = {Optimal Stopping Games and {N}ash Equilibrium}, | |
| journal = {Theory Probability and Applications}, | |
| volume = {53}, | |
| number = {3}, | |
| year = {2008}, | |
| pages = {558-571} | |
| } | |
| @Article{Petrucelli:1980, | |
| author = {Petrucelli, Joseph D.}, | |
| title = {On a Best Choice Problem with Partial Information}, | |
| journal = {The Annals of Statistics}, | |
| volume = {8}, | |
| number = {5}, | |
| year = {1980}, | |
| pages = {1171-1174} | |
| } | |
| @Article{Petrucelli:1981, | |
| author = {Petrucelli, Joseph D.}, | |
| title = {Best Choice Problems Involving Uncertainty of Selection and Recall of Observation}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {18}, | |
| year = {1981}, | |
| pages = {415-425} | |
| } | |
| @Article{Petrucelli:1984, | |
| author = {Petrucelli, Joseph D.}, | |
| title = {Best Choice Problems Involving Recall with Uncertainty of Selection when the Number of Observations is Random}, | |
| journal = {Advances in Applied Probability}, | |
| volume = {16}, | |
| year = {1984}, | |
| pages = {111-130} | |
| } | |
| @Article{Pfeifer:1989, | |
| author = {Pfeifer, Dietmar}, | |
| title = {Extremal Processes, Secretary Problems and the 1/e Law}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {26}, | |
| number = {4}, | |
| year = {1989}, | |
| month = {December}, | |
| pages = {722--733}, | |
| abstract = {We consider a class of secretary problems in which the order of arrival of candidates is no longer uniformly distributed. By a suitable embedding in a time-transformed extremal process it is shown that the asymptotic winning probability is again $1/e$ as in the classical situation. Extensions of the problem to more than one choice are also considered.} | |
| } | |
| @Article{Pisinger:1997, | |
| author = {Pisinger, David}, | |
| title = {A Minimal Algorithm for the 0-1 Knapsack Problem}, | |
| journal = {Operations Research}, | |
| volume = {45}, | |
| number = {5}, | |
| year = {1997}, | |
| pages = {758--767} | |
| } | |
| @Article{Porosinski:1987, | |
| author = {Porosinski, Zdzislaw}, | |
| title = {The Full-Information Best Choice Problem with a Random Number of Observations}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {24}, | |
| number = {2}, | |
| year = {1987}, | |
| pages = {293-307}, | |
| abstract = {The full-information best choice problem with a random number of observations is considered. N i.i.d. random variables with a known continuous distribution are observed sequentially with the object of selecting the largest. Neither recall nor uncertainty of selection is allowed and one choice must be made. In this paper the number N of observations is random with a known distribution. The structure of the stopping set is investigated. A class of distributions of N (which contains in particular the uniform, negative-binomial and Poisson distributions) is determined, for which the so-called “monotone case” occurs. The theoretical solution for the monotone case is considered. In the case where N is geometric the optimal solution is presented and the probability of winning worked out. Finally, the case where N is uniform is examined. A simple asymptotically optimal stopping rule is found and the asymptotic probability of winning is obtained.} | |
| } | |
| @Article{Porosinski:2002, | |
| author = {Porosinski, Zdzislaw}, | |
| title = {On Best Choice Problems Having Similar Solutions}, | |
| journal = {Statistics and Probability Letters}, | |
| volume = {56}, | |
| number = {3}, | |
| year = {2002}, | |
| pages = {321-327}, | |
| abstract = {The purpose of the paper is to point out that best choice problems with different information structure may have similar solutions. A full-information best choice problem with a random number of objects having uniform distribution is considered. An optimal stopping rule, determined by decreasing sequence of levels, is found. Asymptotic behaviour of both an optimal stopping rule and a winning probability is examined in detail. Both the sequence of optimal levels determining optimal strategies and asymptotic winning probabilities are the same in the considered problem as well as in a best choice problem with partial information considered by Petruccelli (Ann. Statist. 8 (1980) 1171–1174).} | |
| } | |
| @Article{Porosinski:2003, | |
| author = {Porosinski, Zdzislaw}, | |
| title = {On Optimal Choosing of One of the $k$ Best Objects}, | |
| journal = {Statistics and Probability Letters}, | |
| volume = {65}, | |
| number = {4}, | |
| year = {2003}, | |
| pages = {419-432}, | |
| abstract = {A full-information continuous-time best choice problem is considered. A stream of objects being iid random variables with a known continuous distribution function is observed. The objects appear according to some renewal process independent of objects. The objective is to maximize the probability of selecting of one of the k best objects when observation is perfect, one choice can be made and neither recall nor uncertainty of selection is allowed. The horizon of observation is a positive random variable independent of objects. The natural case of a Poisson renewal process (with intensity λ) and of exponentially distributed horizon (with parameter μ) is examined in detail. An optimal stopping rule stops at the first object which is greater than some constant level c(p) depending only on p=μ/(μ+λ). The probability of choosing the proper object P(win) is constant for all natural cases, i.e. when p is small. Simple formulae and numerical values for c(p) and P(win) are obtained. It is interesting that if p tends to 0, P(win) goes to 1 and c(p) goes to 0 at a much slower rate than exponentially fast.} | |
| } | |
| @Incollection{Porosinski:2004, | |
| author = {Porosinski, Zdzislaw}, | |
| title = {Modified Strategies in a Competitive Best Choice Problem with Random Priority}, | |
| booktitle = {Advances in Dynamic Games}, | |
| editor = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {7}, | |
| year = {2004}, | |
| pages = {249--256} | |
| } | |
| @Incollection{Porosinski:2005, | |
| author = {Porosinski, Zdzislaw}, | |
| title = {Modified Strategies in a Competitive Best Choice Problem with Random Priority}, | |
| booktitle = {Advances in Dynamic Games}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| editor = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {7}, | |
| year = {2005}, | |
| pages = {263-270} | |
| } | |
| @Article{Porosinski:Szajowski:1996, | |
| author = {Porosinski, Zdzislaw and Szajowski, Krzysztof}, | |
| title = {On Continuous-Time Two Person Full-Information Best Choice Problem with Imperfect Observation}, | |
| journal = {The Indian Journal of Statistics}, | |
| volume = {58}, | |
| number = {2}, | |
| year = {1996}, | |
| month = {June}, | |
| pages = {186-193} | |
| } | |
| @Article{Preater:1994, | |
| author = {Preater, J.}, | |
| title = {On Multiple Choice Secretary Problems}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {19}, | |
| number = {3}, | |
| year = {1994}, | |
| pages = {597--602} | |
| } | |
| @Article{Preater:1998, | |
| author = {Preater, J.}, | |
| title = {A Dynamic Recruitment Problem}, | |
| journal = {IMA Journal of Management Mathematics}, | |
| volume = {9}, | |
| number = {1}, | |
| year = {1998}, | |
| pages = {19--34}, | |
| abstract = {We introduce a sequential recruitment problem in which the employee pool needs continual replenishment due to random depletions of personnel. We determine an optimal selection policy and discuss its monotonicity and asymptotic properties.} | |
| } | |
| @Article{Preater:1999, | |
| author = {Preater, J.}, | |
| title = {The Best-Choice Problem for Partially Ordered Objects}, | |
| journal = {Operations Research Letters}, | |
| volume = {25}, | |
| number = {4}, | |
| year = {1999}, | |
| pages = {187--190}, | |
| abstract = {We consider the problem of making a single on-line selection from a random sequence of partially ordered objects. We show that, as long as the number of objects is given in advance, the selector can pick a maximal one with probability at least $1/8$, without prior knowledge of the partial order.} | |
| } | |
| @Article{Presman:Sonin:1972, | |
| author = {Presman, E. L. and Sonin, I. M.}, | |
| title = {The Best Choice Problem for a Random Number of Objects}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {17}, | |
| number = {4}, | |
| year = {1972}, | |
| pages = {657--668} | |
| } | |
| @Article{Presman:Sonin:1975, | |
| author = {Presman, E. L. and Sonin, I. M.}, | |
| title = {Equilibrium Points in a Game Related to the Best Choice Problem}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {20}, | |
| number = {4}, | |
| year = {1975}, | |
| pages = {770-781} | |
| } | |
| @Article{Presman:Sonin:2010, | |
| author = {Presman, E. L. and Sonin, I. M.}, | |
| title = {On Optimal Stopping of Random Sequences Modulated by {M}arkov Chains}, | |
| journal = {Theory of Probability and its Applications}, | |
| volume = {54}, | |
| number = {3}, | |
| year = {2010}, | |
| pages = {534-542} | |
| } | |
| @Article{Przykucki:Sulkowska:2010, | |
| author = {Michal Przykucki and Malgorzata Sulkowska}, | |
| title = {{G}usein-{Z}ade problem for Directed Path}, | |
| journal = {Discrete Optimization}, | |
| volume = {7}, | |
| number = {1-2}, | |
| year = {2010}, | |
| pages = {13-20}, | |
| abstract = {We consider the following online decision problem. The vertices of a directed path are being observed one by one in some random order by a selector. At time t the selector examines the t th vertex and knows the graph induced by the t vertices that have already been examined. The selector’s aim is to choose the currently examined vertex maximizing the probability that it belongs to some prescribed subset of vertices. The optimal stopping time for a subset consisting of the two top vertices is given. For the path of cardinality n the numerical approximation of the probability of the right choice according to the optimal algorithm is given.} | |
| } | |
| @Article{Quine:1980, | |
| author = {Quine, M. P.}, | |
| title = {Three Limit Theorems for Scores Based on Occupancy Numbers}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {8}, | |
| number = {1}, | |
| year = {1980}, | |
| month = {February}, | |
| pages = {148-156} | |
| } | |
| @Article{Quine:Robinson:1984, | |
| author = {Quine, M. P. and Robinson, J.}, | |
| title = {Three Limit Theorems for Scores Based on Occupancy Numbers}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {12}, | |
| number = {3}, | |
| year = {1984}, | |
| month = {August}, | |
| pages = {794-804} | |
| } | |
| @Article{Quine:Law:1996, | |
| author = {Quine, M. P. and Law, J. S.}, | |
| title = {Exact Results for a Secretary Problem}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {33}, | |
| year = {1996}, | |
| pages = {630-639}, | |
| abstract = {We consider the following secretary problem: items ranked from 1 to are randomly selected without replacement. one at a time. and to 'win' is to stop at an item whose overall rank is less than or equal to given only the relative ranks of the items drawn so far. Our method of analysis is based on the existence of an imbedded Markov chain and uses the technique of backwards induction. In principal the approach can be used to give exact results for any value of $s$; we do the working for $s = 3$. We give exact results for the optimal strategy, the probability of success and the distribution of T, and the total number of draws when the optimal strategy is implemented. We also give some asymptotic results for these quantities as $n \rightarrow x$.} | |
| } | |
| @Article{Radzik:Szajowski:1988, | |
| author = {Radzik and Szajowski}, | |
| title = {On Some Sequential Game}, | |
| journal = {Pure and Applied Mathematical Science}, | |
| volume = {28}, | |
| number = {}, | |
| year = {1988}, | |
| pages = {51--63} | |
| } | |
| @Article{Radzik:Szajowski:1990, | |
| author = {Radzik and Szajowski}, | |
| title = {Sequential Games with Random Priority}, | |
| journal = {Sequential Analysis}, | |
| publisher = {Taylor and Francis}, | |
| volume = {9}, | |
| number = {4}, | |
| year = {1990}, | |
| pages = {361-377}, | |
| abstract = {The paper deals with a class of two-person zero-sum sequential games related to a partial observation of random variables $X_1,X_2,...,X_N$ by the players. Each player, based on some indirect information, selects a moment $t$, $l\leq t \leq N$. In this way he communicates that he would like to accept an unknown realization $x_t$ of $X_t$. When only one player selects the moment t then he obtains the required realization. If both players select the same moment t, then there is a lottery choosing either Player 1 or Player 2. The player chosen by the lottery obtains the realization xt and the player thus deprived of the acceptance of $x_t$ at $t<N$, may select any later realization. Each player can accept only one realization. Payoff functions of the players depend on the realizations chosen by them. The normal form of the game is constructed and a solution is given with the help of the help of the dynamic programming method. The results are illustrated by examples.} | |
| } | |
| @Article{Ramsey:2008, | |
| author = {Ramsey, David M.}, | |
| title = {A Large Population Job Search Game with Discrete Time}, | |
| journal = {European Journal of Operational Research}, | |
| volume = {188}, | |
| number = {2}, | |
| year = {2008}, | |
| month = {July}, | |
| pages = {586--602}, | |
| abstract = {A job search problem is considered, in which there is a large population of jobs initially available and a large population of searchers. The ratio of the number of searchers to the number of jobs is α. Each job has an associated value from a known distribution. At each of N moments the searchers observe a job, whose value comes from the distribution of the values of currently available jobs. If a searcher accepts a job, s/he ceases searching and the job becomes unavailable. Hence, the distribution of the values of available jobs changes over time. Also, the ratio of the number of those still searching to the number of available jobs changes. The model is presented and Nash equilibrium strategies for such problems are considered. By definition, when all the population use a Nash equilibrium strategy, the optimal response of an individual is to use the same strategy. Conditions are given that ensure the existence of a unique Nash equilibrium strategy. Examples are given to illustrate the model and present different approaches to solving such problems.} | |
| } | |
| @Incollection{Ramsey:2011, | |
| author = {Ramsey, David M.}, | |
| title = {Mutual Mate Choice with Multiple Criteria}, | |
| booktitle = {Advances in Dynamic Games}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| editor = {Breton, Michele and Szajowski, Krzysztof}, | |
| publisher = {Birkhauser Boston}, | |
| volume={11}, | |
| year = {2011}, | |
| pages = {337-355} | |
| } | |
| @Incollection{Ramsey:Cierpial:2009, | |
| author = {Ramsey, David M. and Cierpial, Diana}, | |
| title = {Cooperative Strategies in Stopping Games}, | |
| booktitle = {Advances in Dynamic Games and Their Applications}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| editor = {Pourtallier, Odile and Gaitsgory, Vladimir and Bernhard, Pierre}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {10}, | |
| year = {2009}, | |
| pages = {1-16} | |
| } | |
| @Article{Ramsey:Szajowski:2001, | |
| author = {Ramsey, David M. and Szajowski, Krzyszstof}, | |
| title = {Three-Person Stopping Game with Players Having Privileges}, | |
| journal = {Journal of Mathematical Sciences}, | |
| publisher = {Plenum Publishing Corporation}, | |
| volume = {105}, | |
| number = {6}, | |
| year = {2001}, | |
| pages = {2599--2608} | |
| } | |
| @Incollection{Ramsey:Szajowski:2004, | |
| author = {Ramsey, David M. and Szajowski, Krzyszstof}, | |
| title = {Bilateral Approach to the Secretary Problem}, | |
| booktitle = {Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control}, | |
| editor = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| publisher = {Birkhauser}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| year = {2004}, | |
| pages = {271--284} | |
| } | |
| @Incollection{Ramsey:Szajowski:2006, | |
| author = {Ramsey, David M. and Szajowski, Krzyszstof}, | |
| title = {Correlated Equilibria in Competitive Staff Selection Problem}, | |
| booktitle = {Game Theory and Mathematical Economics}, | |
| series = {Banach Center Publications}, | |
| publisher = {Polish Academy of Sciences, Warsaw, Poland}, | |
| year = {2006}, | |
| pages = {253-265} | |
| } | |
| @Article{Ramsey:Szajowski:2008, | |
| author = {Ramsey, David M. and Szajowski, Krzyszstof}, | |
| title = {Selection of a Correlated Equilibrium in {M}arkov Stopping Games}, | |
| journal = {European Journal of Operational Research}, | |
| publisher = {Elsevier Sciences Ltd}, | |
| volume = {184}, | |
| number = {1}, | |
| year = {2008}, | |
| pages = {185--206} | |
| } | |
| @Article{Rapoport:Seale:Winter:2002, | |
| author = {Rapoport, Amnon and Seale, Darryl A. and Winter, Eyal}, | |
| title = {Coordination and Learning Behavior in Large Groups with Asymmetric Players}, | |
| journal = {Games and Economic Behavior}, | |
| volume = {39}, | |
| number = {1}, | |
| year = {2002}, | |
| pages = {111--136}, | |
| abstract = {We study a class of large-group, noncooperative, iterated market entry games with complete information, binary choices, and asymmetric players in which the incentive of each player to enter the market decreases the larger the number of entrants. Experimental results from two different studies show remarkable coordination on the aggregate level, which is accounted for successfully by the Nash equilibrium solution. The equilibrium solution is less successful in accounting for the differences among types of players with differential entry costs or differences among players of the same type. Rather, the behavioral patterns observed on the aggregate level are accounted for by a reinforcement-based learning model postulating an initial distribution of individual cutoff points. These cutoff points are assumed to change over time, at a decreasing rate, as a joint function of the decision and outcome of the preceding period.} | |
| } | |
| @Article{Rasmussen:Pliska:1976, | |
| author = {Rasmussen, Willis T. and Pliska, Stanley R.}, | |
| title = {Choosing the Maximum from a Sequence with a Discount Function}, | |
| journal = {Applied Mathematics and Optimization}, | |
| volume = {2}, | |
| number = {3}, | |
| year = {1976}, | |
| pages = {279--289} | |
| } | |
| @Article{Rasmussen:1975, | |
| author = {Rasmussen, Willis T.}, | |
| title = {A Generalized Choice Problem}, | |
| journal = {Journal of Optimization Theory and Applications}, | |
| publisher = {Kluwer Academic Publishers-Plenum Publishers}, | |
| volume = {15}, | |
| number = {3}, | |
| year = {1975}, | |
| pages = {311--325} | |
| } | |
| @Article{Rasmussen:Pliska:1975, | |
| author = {Rasmussen, Willis T. and Pliska, Stanley R.}, | |
| title = {Choosing the Maximum from a Sequence with a Discount Function}, | |
| journal = {Applied Mathematics and Optimization}, | |
| publisher = {Springer-Verlag}, | |
| volume = {2}, | |
| number = {3}, | |
| year = {1975}, | |
| pages = {279--289} | |
| } | |
| @Article{Ravindran:Szajowski:1992, | |
| author = {Ravindran and Szajowski}, | |
| title = {Non-Zero Sum Game with Priority as {D}ynkin's Game}, | |
| journal = {Mathematica Japonica}, | |
| volume = {37}, | |
| number = {3}, | |
| year = {1992}, | |
| pages = {401--413} | |
| } | |
| @Article{Renault:Solan:Vieille:2013, | |
| author = {Renault, Jerome and Solan, Eilon and Vieille, Nicolas}, | |
| title = {Dynamic Sender-Receiver Games}, | |
| journal = {Journal of Economic Theory}, | |
| volume = {148}, | |
| number = {}, | |
| year = {2013}, | |
| pages = {502--534} | |
| } | |
| @Article{Righter:2011, | |
| author = {Righter,Rhonda}, | |
| title = {Stochastic Sequential Assignment Problem with Arrivals}, | |
| journal = {Probability in the Engineering and Informational Sciences}, | |
| volume = {25}, | |
| number = {4}, | |
| year = {2011}, | |
| month = {October}, | |
| pages = {477--485} | |
| } | |
| @Article{Rinott:SamuelCahn:1987, | |
| author = {Rinott, Yosef and Samuel-Cahn, Ester}, | |
| title = {Comparisons of Optimal Stopping Values and Prophet Inequalities for Negatively Dependent Random Variables}, | |
| journal = {The Annals of Statistics}, | |
| volume = {15}, | |
| number = {4}, | |
| year = {1987}, | |
| month = {December}, | |
| pages = {1482--1490} | |
| } | |
| @Incollection{Rinott:SamuelCahn:1992, | |
| author = {Rinott, Yosef and Samuel-Cahn, Ester}, | |
| title = {Optimal Stopping Values and Prophet Inequalities for Some Dependent Random Variables}, | |
| booktitle = {Stochastic inequalities}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Lecture Notes -- Monograph Series}, | |
| volume = {22}, | |
| year = {1992}, | |
| month = {}, | |
| pages = {343--358} | |
| } | |
| @Article{Robbins:1956, | |
| author = {Robbins, Herbert}, | |
| title = {A Sequential Decision Problem with a Finite Memory}, | |
| journal = {Proceedings of the National Academy of Sciences of the United States of America}, | |
| publisher = {National Academy of Sciences}, | |
| volume = {42}, | |
| number = {12}, | |
| year = {1956}, | |
| pages = {920--923} | |
| } | |
| @Article{Robbins:1970, | |
| author = {Robbins, Herbert}, | |
| title = {Statistical Methods Related to the Law of the Iterated Logarithm}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {41}, | |
| number = {5}, | |
| year = {1970}, | |
| month = {October}, | |
| pages = {1397--1409} | |
| } | |
| @Article{Robbins:Monro:1951, | |
| author = {Robbins, Herbert and Monro, Sutton}, | |
| title = {A Stochastic Approximation Method}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {22}, | |
| number = {3}, | |
| year = {1951}, | |
| month = {September}, | |
| pages = {400--407} | |
| } | |
| @Article{Robbins:Siegmund:1970, | |
| author = {Robbins, Herbert and Siegmund, David O.}, | |
| title = {Boundary Crossing Probabilities for the Wiener Process and Sample Sums}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {41}, | |
| number = {5}, | |
| year = {1970}, | |
| month = {October}, | |
| pages = {1410--1429} | |
| } | |
| @Article{Robbins:Siegmund:1974a, | |
| author = {Robbins, Herbert and Siegmund, David O.}, | |
| title = {The Expected Sample Size of Some Tests of Power One}, | |
| journal = {The Annals of Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {2}, | |
| number = {3}, | |
| year = {1974}, | |
| month = {May}, | |
| pages = {415--436} | |
| } | |
| @Article{Robbins:Siegmund:1974b, | |
| author = {Robbins, Herbert and Siegmund, David O.}, | |
| title = {Sequential Tests Involving Two Populations}, | |
| journal = {Journal of the American Statistical Association}, | |
| volume = {69}, | |
| number = {345}, | |
| year = {1974}, | |
| pages = {132--139}, | |
| abstract = {For testing which of two normally distributed treatments with a common variance is ``superior'' (has a larger mean response), we give a class of sequential probability ratio tests whose error probability functions are essentially independent of the sampling rule used. It is shown that the expected number of observations on the ``inferior'' treatment must be at least one-half that required by pairwise sampling, and a class of sampling rules is given which for some parameter values and significance levels almost attains this theoretical bound.} | |
| } | |
| @Incollection{Robbins:Siegmund:1976, | |
| author = {Robbins, Herbert and Siegmund, David O.}, | |
| title = {Sequential Estimation of $p$ in Bernoulli Trials}, | |
| booktitle = {Studies in Probability and Statistics, Papers in Honour of Edwin J. G. Pitman}, | |
| editor = {Williams, E. J.}, | |
| publisher = {North-Holland, Amsterdam}, | |
| year = {1976}, | |
| pages = {103--107} | |
| } | |
| @Article{Rocha:1993, | |
| author = {Rocha, Amy L.}, | |
| title = {The Infinite Secretary Problem with Recall}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {21}, | |
| number = {2}, | |
| year = {1993}, | |
| month = {April}, | |
| pages = {898--916} | |
| } | |
| @Article{Rogerson:1987, | |
| author = {Rogerson, Peter A.}, | |
| title = {Probabilities of Choosing Applicants of Arbitrary Rank in the Secretary Problem}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {24}, | |
| year = {1987}, | |
| pages = {527--533} | |
| } | |
| @Article{Rogerson:1988, | |
| author = {Rogerson, Peter A.}, | |
| title = {Alternative Strategies for Selling Land to the Highest Bidder}, | |
| journal = {Environment and Planning A}, | |
| volume = {20}, | |
| number = {6}, | |
| year = {1988}, | |
| month = {June}, | |
| pages = {817--828}, | |
| abstract = {In this paper the properties of several models of sequential bidding behavior are evaluated. In particular, the returns to a seller who maximizes the probability of selling to the highest bidder are compared with the returns of a rank minimization strategy which is more conservative. The comparison reveals that the rank minimization strategy will generally lead to shorter waiting times, higher expected selling prices, and lower probabilities of receiving the worst bids. Both of these objectives assume that sellers have no initial information pertaining to the distribution of bid prices. This is in sharp contrast to the more usual assumption of complete information about the parameters of the distribution. The losses associated with not having a priori information on the number of bidders are also evaluated. Under such circumstances, sellers may adopt more conservative strategies, with the consequent result of shorter waiting times and lower expected prices.} | |
| } | |
| @Article{Rose:1982a, | |
| author = {Rose, John S.}, | |
| title = {Selection of Nonextremal Candidates from a Random Sequence}, | |
| journal = {Journal of Optimization Theory and Applications}, | |
| volume = {38}, | |
| number = {2}, | |
| year = {1982}, | |
| pages = {207-219} | |
| } | |
| @Article{Rose:1982b, | |
| author = {Rose, John S.}, | |
| title = {A Problem of Optimal Choice and Assignment}, | |
| journal = {Operations Research}, | |
| volume = {30}, | |
| number = {1}, | |
| year = {1982}, | |
| pages = {172-181} | |
| } | |
| @Article{Rose:1982c, | |
| author = {Rose, John S.}, | |
| title = {Twenty Years of Secretary Problems: A Survey of Optimal Choice}, | |
| journal = {Management Studies}, | |
| volume = {1}, | |
| number = {}, | |
| year = {1982}, | |
| pages = {53--64} | |
| } | |
| @Article{Rose:1984, | |
| author = {Rose, John S.}, | |
| title = {Optimal Sequential Selection Based on Relative Ranks with Renewable Call Options}, | |
| journal = {Journal of the American Statistical Association}, | |
| volume = {79}, | |
| number = {386}, | |
| year = {1984}, | |
| month = {June}, | |
| pages = {430-435} | |
| } | |
| @Article{Rosenberg:Solan:Vieille:2001, | |
| author = {Rosenberg, Dinah and Solan, Eilon and Vieille, Nicolas}, | |
| title = {Stopping Games with Randomized Strategies}, | |
| journal = {Probability Theory and Related Fields}, | |
| volume = {119}, | |
| number = {}, | |
| year = {2001}, | |
| pages = {433-451} | |
| } | |
| @Article{Rosenberg:Solan:Vieille:2004, | |
| author = {Rosenberg, Dinah and Solan, Eilon and Vieille, Nicolas}, | |
| title = {Stochastic Games with a Single Controller and Incomplete Information}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {43}, | |
| number = {1}, | |
| year = {2004}, | |
| pages = {86-110} | |
| } | |
| @Article{Rubin:Samuels:1977, | |
| author = {Rubin, Herman and Samuels, Stephen M.}, | |
| title = {The Finite-Memory Secretary Problem}, | |
| journal = {The Annals of Probability}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {5}, | |
| number = {4}, | |
| year = {1977}, | |
| month = {August}, | |
| pages = {627--635}, | |
| abstract = {The expected rank of the individual selected in the secretary problem can be kept bounded as the number of individuals becomes infinite even if we are not permitted to remember more than one individual at a time. The least upper bound of these expected ranks is derived: it is approximately 7.4.} | |
| } | |
| @Article{Saario:1987, | |
| author = {Saario, Vesa}, | |
| title = {Comparison of the Discrete and Continuous-Time Stochastic Selling Models}, | |
| journal = {Engineering Costs and Production Economics}, | |
| issue = {Special Issue Proceedings of the Fourth International Working Seminar on Production Economics}, | |
| volume = {12}, | |
| number = {1}, | |
| year = {1987}, | |
| pages = {15-20}, | |
| abstract = {The problem of determining the optimal selling times for units of some property is considered. The models are developed for both discrete and continuous-time cases, their optimal decision rules are derived and their asymptotic characteristics are analyzed and discussed.} | |
| } | |
| @Article{Saario:1989, | |
| author = {Saario, Vesa}, | |
| title = {Some Properties of the Sequential {M}arkovian Allocation Problem}, | |
| journal = {Engineering Costs and Production Economics}, | |
| volume = {17}, | |
| number = {1-4}, | |
| year = {1989}, | |
| pages = {175-182}, | |
| abstract = {This paper deals with a stochastic allocation problem associated with the Markov chain. The object is to maximize the expected present value of the sum of the values of the random variables sampled from the process. The maximum number of the allocation units is fixed and the decision to accept or reject the current observation is based on the known and unknown transition probabilities. The problem is formulated and the optimal decision rule derived by the technique of dynamic programming. Certain computational aspects of the optimal decision rule with some numerical results are also presented, and finally, some promising real-life applications and extensions of the models are discussed.} | |
| } | |
| @Incollection{Sackrowitz:SamuelCahn:1992, | |
| author = {Sackrowitz, Harold and Samuel-Cahn, Ester}, | |
| title = {Evaluating the Chosen Population: a Bayes and Minimax Approach}, | |
| booktitle = {Adaptive statistical procedures and related topics}, | |
| editor = {Van Ryzin, John}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Lecture Notes--Monograph Series}, | |
| volume = {8}, | |
| year = {1986}, | |
| pages = {386--399} | |
| } | |
| @Article{Sakaguchi:1973, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Optimal Stopping in Sampling From a Bivariate Distribution}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {16}, | |
| number = {3}, | |
| year = {1973}, | |
| pages = {186-200} | |
| } | |
| @Article{Sakaguchi:1977, | |
| author = {Sakaguchi, Minoru}, | |
| title = {A Sequential Allocation Game for Targets with Varying Values}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {20}, | |
| number = {3}, | |
| year = {1977}, | |
| month = {September}, | |
| pages = {182-193} | |
| } | |
| @Article{Sakaguchi:1978, | |
| author = {Sakaguchi, Minoru}, | |
| title = {When To Stop: Randomly Appearing Bivariate Target Values}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {21}, | |
| number = {1}, | |
| year = {1978}, | |
| month = {March}, | |
| pages = {45-57} | |
| } | |
| @Article{Sakaguchi:1980, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Non-Zero-Sum Games Related to the Secretary Problem}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {23}, | |
| number = {3}, | |
| year = {1980}, | |
| month = {September}, | |
| pages = {287-292} | |
| } | |
| @Article{Sakaguchi:1988a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Some Infinite Problem in Classical Secretary Problems}, | |
| journal = {Mathematica Japonica}, | |
| volume = {34}, | |
| year = {1988}, | |
| pages = {307-318} | |
| } | |
| @Article{Sakaguchi:1988b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Some Two-Person Bilateral Games in the Generalized Secretary Problem}, | |
| journal = {Mathematica Japonica}, | |
| volume = {34}, | |
| year = {1988}, | |
| pages = {637-654} | |
| } | |
| @Article{Sakaguchi:1995a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Optimal Stopping Games for Bivariate Uniform Distribution}, | |
| journal = {Mathematica Japonica}, | |
| volume = {41}, | |
| year = {1995}, | |
| pages = {677-687} | |
| } | |
| @Article{Sakaguchi:1995b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Optimal Stopping Games - A Review}, | |
| journal = {Mathematica Japonica}, | |
| volume = {42}, | |
| year = {1995}, | |
| pages = {343-351} | |
| } | |
| @Article{Sakaguchi:1998, | |
| author = {Sakaguchi, Minoru}, | |
| title = {A Non-Zero-Sum Repeated Game -- Criminal vs. Police}, | |
| journal = {Mathematica Japonica}, | |
| volume = {48}, | |
| year = {1998}, | |
| pages = {427-436} | |
| } | |
| @Article{Sakaguchi:2001a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Three-Person Stopping Games Under Winning Probability Maximization and Players' Unequally Weighted Privilege}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {4}, | |
| year = {2001}, | |
| pages = {279-295} | |
| } | |
| @Article{Sakaguchi:2001b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {A Best-Choice Problem for a Production System which Deteriorates at a Disorder Time}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {4}, | |
| year = {2001}, | |
| pages = {689-698} | |
| } | |
| @Article{Sakaguchi:2002a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Better-Than-Opponent - A Stopping Game for Poisson-Arriving Offers}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {6}, | |
| year = {2002}, | |
| pages = {279-295} | |
| } | |
| @Article{Sakaguchi:2002b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Equilibrium in No-Information Best-Choice Games Played by Equally Weighted Players}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {6}, | |
| year = {2002}, | |
| pages = {297-305} | |
| } | |
| @Article{Sakaguchi:2002c, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Multi-Round Card Game With Arbitration and Random Amount of Bet}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {6}, | |
| year = {2002}, | |
| pages = {505-511} | |
| } | |
| @Article{Sakaguchi:2003a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Non-Zero-Sum Best-Choice Games Where Two Stops Are Required}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {8}, | |
| year = {2003}, | |
| pages = {165-176} | |
| } | |
| @Article{Sakaguchi:2003b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {MultiStage Non-Zero-Sum Arbitration Game}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {8}, | |
| year = {2003}, | |
| pages = {177-183} | |
| } | |
| @Article{Sakaguchi:2004a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Three-Person Games of Odd-Man-Wins}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {1-11} | |
| } | |
| @Article{Sakaguchi:2004b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Equilibrium in Two-Player Games of Showcase Showdown}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {37-43} | |
| } | |
| @Article{Sakaguchi:2004c, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Optimal Sequential Decisions with Information Invariance}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {181-191} | |
| } | |
| @Article{Sakaguchi:2004d, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Equilibrium in the Three-Player Game of ``Risky Exchange''}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {199-208} | |
| } | |
| @Article{Sakaguchi:2004e, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Multi-Stage Three-Person Game with Arbitration}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {339-346} | |
| } | |
| @Article{Sakaguchi:2004f, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Two-Player Games of 'Score Showdown'}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {347-357} | |
| } | |
| @Incollection{Sakaguchi:2004g, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Optimal Stopping Games where Players have Weighted Privilege}, | |
| booktitle = {Advances in Dynamic Games}, | |
| editor = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {7}, | |
| year = {2004}, | |
| pages = {271-279}, | |
| abstract = {A non-zero-sum n-stage game version of a full-information best- choice problem under expected net value (ENV) maximization is analysed and their solutions are obtained in some special cases of 2-person and 3-person games. The essential feature contained in this multistage game is the fact that the players have their own weights by which at each stage one player’s desired decision is preferred to the opponent’s one by drawing a lottery.} | |
| } | |
| @Article{Sakaguchi:2005a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Golden Trisection Numbers and Two-Player Game of Keep-Or-Exchange}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {201-211} | |
| } | |
| @Article{Sakaguchi:2005b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {A Note On Golden Bisection Number and Two-Player Infinite Game}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {449-452} | |
| } | |
| @Article{Sakaguchi:2005c, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Analysis of a Method for Calculating an Economic Order Quantity in Inventory Models}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2004}, | |
| pages = {475-485} | |
| } | |
| @Article{Sakaguchi:2006a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {A Simple Two-Player Two-Sided Game of Deception}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2006}, | |
| pages = {1045-1053} | |
| } | |
| @Article{Sakaguchi:2006b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Poker Games Where Players Have Non-Uniform Hand Distribution}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2006}, | |
| pages = {1195-1207} | |
| } | |
| @Article{Sakaguchi:2006c, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Equilibrium in N-Player Competitive Silent Games of Timing}, | |
| journal = {Game Theory and Applications}, | |
| volume = {}, | |
| year = {2006}, | |
| pages = {188-196} | |
| } | |
| @Article{Sakaguchi:2007a, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Note: A Repeated One-Player Game of Deception with Discounting}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2007}, | |
| pages = {157-159} | |
| } | |
| @Article{Sakaguchi:2007b, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Three Member Committee Where Odd-Man's Judgement Is Paid Regard}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2007}, | |
| pages = {263-268} | |
| } | |
| @Article{Sakaguchi:2008, | |
| author = {Sakaguchi, Minoru}, | |
| title = {Four-Member Committee Looking For a Specialist with Two High Abilities}, | |
| journal = {Scientiae Mathematica Japonicae Online}, | |
| volume = {E}, | |
| year = {2008}, | |
| pages = {317-322} | |
| } | |
| @Article{Sakaguchi:Hamada:2000, | |
| author = {Sakaguchi, Minoru and Hamada, Toshio}, | |
| title = {A Class of Best-Choice Problems On Sequences of Continuous Bivariate Random Variables}, | |
| journal = {Lecture Notes-Monograph Series}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {35}, | |
| year = {2000}, | |
| pages = {111-125}, | |
| abstract = {An employer interviews a finite number n of applicants for a position. They are interviewed one by one sequentially in random order. As each applicant i is interviewed, two attributes are evaluated by the amounts $X_i$ and $Y_i$, where $X_i$'s and $Y_i$'s are not necessarily mutually independent, but $\{(X_{i},Y_{i})\}_{i=1}^{n}$ is iid sequence of continuous bivariate random variables and the common distribution of $(X_i,Y_i)$'s is known. Suppose that the employer is under the condition of full-information secretary problem without recall. We consider two kinds of the employer's objective and for each of the objectives the problems are formulated by dynamic programming and the optimal policy is explicitly derived.} | |
| } | |
| @Article{Sakaguchi:Hamada:2001, | |
| author = {Sakaguchi, Minoru and Hamada, Toshio}, | |
| title = {Optimal Stopping Games Under Winning Probability Maximization and Player's Weighted Privilege}, | |
| journal = {Scientiae Mathematicae Japonicae Online}, | |
| volume = {4}, | |
| year = {2001}, | |
| pages = {267-278} | |
| } | |
| @Article{Sakaguchi:Mazalov:2004, | |
| author = {Sakaguchi, Minoru and Mazalov, Vladimir V.}, | |
| title = {A Non-Zero-Sum No-Information Best-Choice Game}, | |
| journal = {Mathematical Methods of Operations Research}, | |
| volume = {60}, | |
| year = {2004}, | |
| pages = {437-451} | |
| } | |
| @Article{Salminen:Teich:Wallenius:1998, | |
| author = {Salminen, Pekka and Teich, Jeffrey E. and Wallenius, Jyrki}, | |
| title = {The Secretary Problem Revisited - The Group Decision-Making Perspective}, | |
| journal = {Group Decision and Negotiation}, | |
| publisher = {Kluwer Academic Publishers}, | |
| volume = {7}, | |
| number = {1}, | |
| year = {1998}, | |
| month = {December}, | |
| pages = {3--21} | |
| } | |
| @Article{SamuelCahn:1974, | |
| author = {Samuel-Cahn, Ester}, | |
| title = {Asymptotic Distributions for Occupancy and Waiting Time Problems with Positive Probability of Falling Through the Cells}, | |
| journal = {The Annals of Probability}, | |
| volume = {2}, | |
| number = {3}, | |
| year = {1974}, | |
| month = {December}, | |
| pages = {515--521} | |
| } | |
| @Article{SamuelCahn:1984, | |
| author = {Samuel-Cahn, Ester}, | |
| title = {Comparison of Threshold Stop Rules and Maximum for Independent Nonnegative Random Variables}, | |
| journal = {The Annals of Probability}, | |
| volume = {12}, | |
| number = {4}, | |
| year = {1984}, | |
| month = {November}, | |
| pages = {1213--1216} | |
| } | |
| @Article{SamuelCahn:1992, | |
| author = {Samuel-Cahn, Ester}, | |
| title = {A Difference Prophet Inequality for Bounded I.I.D. Variables, with Cost for Observations}, | |
| journal = {The Annals of Probability}, | |
| volume = {20}, | |
| number = {3}, | |
| year = {1992}, | |
| month = {July}, | |
| pages = {1222--1228} | |
| } | |
| @Article{SamuelCahn:1995, | |
| author = {Samuel-Cahn, Ester}, | |
| title = {The Best-Choice Secretary Problem with Random Freeze on Jobs}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {55}, | |
| number = {2}, | |
| year = {1995}, | |
| pages = {315--327} | |
| } | |
| @Article{Samuels:1965, | |
| author = {Samuels, Stephen M.}, | |
| title = {On the Number of Successes in Independent Trials}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {36}, | |
| number = {4}, | |
| year = {1965}, | |
| month = {August}, | |
| pages = {1272--1278}, | |
| abstract = {The distribution of the number of successes in independent trials is shown to be bell-shaped of every order. The most likely number of successes is ``almost uniquely'' determined from the mean number and from the mean plus the largest and smallest probability of success on any trial. Bounds on the distribution function of the number of successes are obtained and extended to an infinite number of trials, including the Poisson distribution.} | |
| } | |
| @Article{Samuels:1969, | |
| author = {Samuels, Stephen M.}, | |
| title = {The {M}arkov Inequality for Sums of Independent Random Variables}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {40}, | |
| number = {6}, | |
| year = {1969}, | |
| month = {December}, | |
| pages = {1980--1984} | |
| } | |
| @Article{Samuels:1985, | |
| author = {Samuels, Stephen M.}, | |
| title = {A Best-Choice Problem With Linear Travel Cost}, | |
| journal = {Journal of the American Statistical Association}, | |
| publisher = {Taylor and Francis, Ltd. on behalf of the American Statistical Association}, | |
| volume = {80}, | |
| number = {390}, | |
| year = {1985}, | |
| month = {June}, | |
| pages = {461-464}, | |
| abstract = {The concepts of sampling cost and recall of previously seen applicants are here combined in a natural way: The best, second best, and so forth, of infinitely many applicants are located at points independently and uniformly distributed on the unit interval. A traveler, observing relative ranks, hopes to select the best applicant, and incurs a cost proportional to the total distance traveled, plus a unit loss if the applicant selected is not overall best. The optimal policy and its risk are derived. A finite version of the problem is also solved.} | |
| } | |
| @Article{Samuels:1992, | |
| author = {Samuels, Stephen M.}, | |
| title = {Secretary Problems as a Source of Benchmark Bounds}, | |
| journal = {Lecture Notes -- Monograph Series -- Stochastic Inequalities}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {22}, | |
| year = {1992}, | |
| pages = {371--387}, | |
| abstract = {Secretary problems are those sequential selection problems in which the payoff (or cost) depends on the observations only through their ranks. A subclass of such problems allows only selection rules based on relative ranks. The performance of such rules provides readily accessible lower bounds for procedures based on more information. Included here are familiar bounds, like $1/e$; well-known bounds, like $3.8695$; and brand-new bounds, like $2.6003$.} | |
| } | |
| @Article{Samuels:2004, | |
| author = {Samuels, Stephen M.}, | |
| title = {Why Do These Quite Different Best-Choice Problems Have the Same Solutions?}, | |
| journal = {Advances in Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {36}, | |
| number = {2}, | |
| year = {2004}, | |
| pages = {398--416}, | |
| abstract = {The full-information best-choice problem, as posed by Gilbert and Mosteller in 1966, asks us to find a stopping rule which maximizes the probability of selecting the largest of a sequence of $n$ i.i.d. standard uniform random variables. Porosinski, in 1987, replaced a fixed $n$ by a random $N$, uniform on $\{1,2,... ,n\}$ and independent of the observations. A partial-information problem, imbedded in a 1980 paper of Petruccelli, keeps n fixed but allows us to observe only the sequence of ranges (max - min), as well as whether or not the current observation is largest so far. Recently, Porosinski compared the solutions to his and Petruccelli's problems and found that the two problems have identical optimal rules as well as risks that are asymptotically equal. His discovery prompts the question: why? This paper gives a good explanation of the equivalence of the optimal rules. But even under the lens of a planar Poisson process model, it leaves the equivalence of the asymptotic risks as somewhat of a mystery. Meanwhile, two other problems have been shown to have the same limiting risks: the full-information problem with the (suboptimal) Porosinski-Petruccelli stopping rule, and the full-information 'duration of holding the best' problem of Ferguson, Hardwick and Tamaki, which turns out to be nothing but the Porosinski problem in disguise.} | |
| } | |
| @Article{Samuels:Steele:1981, | |
| author = {Samuels, Stephen M. and Steele, J. Michael}, | |
| title = {Optimal Sequential Selection of a Monotone Sequence From a Random Sample}, | |
| journal = {The Annals of Probability}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| volume = {9}, | |
| number = {6}, | |
| year = {1981}, | |
| month = {December}, | |
| pages = {937--947}, | |
| abstract = {The length of the longest monotone increasing subsequence of a random sample of size $n$ is known to have expected value asymptotic to $2n^{1/2}$. We prove that it is possible to make sequential choices which give an increasing subsequence of expected length asymptotic to $(2n)^{1/2}$. Moreover, this rate of increase is proved to be asymptotically best possible.} | |
| } | |
| @Article{Schilling:2012, | |
| author = {Schilling, Mark F.}, | |
| title = {The Surprising Predictability}, | |
| journal = {Mathematics Magazine}, | |
| volume = {85}, | |
| number = {2}, | |
| pages = {141--149}, | |
| publisher = {Mathematical Association of America}, | |
| year = {2012}, | |
| abstract = {Summary When data arise from a situation that can be modeled as a collection of n independent Bernoulli trials with success probability p, a simple rule of thumb predicts the approximate length that the longest run of successes will have, often with remarkable accuracy. The distribution of this longest run is well approximated by an extreme value distribution. In some cases we can practically guarantee the length that the longest run will have. Applications to coin and die tossing, roulette, state lotteries and the digits of π are given.} | |
| } | |
| @Article{Seale:Rapoport:1997, | |
| author = {Seale, Darryl A. and Rapoport, Amnon}, | |
| title = {Sequential Decision Making with Relative Ranks: An Experimental Investigation of the ``Secretary Problem''}, | |
| journal = {Organizational Behavior and Human Decision Processes}, | |
| volume = {69}, | |
| number = {3}, | |
| year = {1997}, | |
| pages = {221--236}, | |
| abstract = {The ``secretary problem'' models a class of optimal stopping decision tasks in which the binary decision to either stop or continue the search only depends on relative ranks. We present this problem in a computer-controlled experiment designed to investigate sequential observation and selection behavior in the context of employer hiring decisions. Our principal objectives are to test the descriptive power of the optimal decision policy; characterize and competitively test simple decision rules, or heuristics, that individuals might use in optimal stopping decision tasks; and examine the sensitivity of the various decision rules by computer simulation. Our simulation results show that the optimal policy is insensitive to moderate deviations from the optimal cutoff value, and that a simple, non-optimal decision rule that counts the number of successive non-candidates performs remarkably well. Model comparisons show that simple cutoff decision rules account for the decisions of the majority of the subjects. The observed tendency to stop the search too early is accounted for by postulating an endogenous cost of time spent in the search.} | |
| } | |
| @Article{Seale:Rapoport:2000, | |
| author = {Seale, Darryl A. and Rapoport, Amnon}, | |
| title = {Optimal Stopping Behavior with Relative Ranks: the Secretary Problem with Unknown Population Size}, | |
| journal = {Journal of Behavioral Decision Making}, | |
| publisher = {John Wiley and Sons, Ltd.}, | |
| volume = {13}, | |
| number = {4}, | |
| year = {2000}, | |
| pages = {391--411} | |
| } | |
| @Article{Shapley:1953, | |
| author = {Shapley, Lloyd}, | |
| title = {Stochastic Games}, | |
| journal = {Proceedings of the National Academy of Sciences}, | |
| volume = {39}, | |
| number = {}, | |
| year = {1953}, | |
| pages = {1095-1100} | |
| } | |
| @Article{Shepp:1969, | |
| author = {Shepp, Larry A.}, | |
| title = {Explicit Solutions to Some Problems of Optimal Stopping}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {40}, | |
| number = {3}, | |
| year = {1969}, | |
| month = {June}, | |
| pages = {993-1010} | |
| } | |
| @Article{Shepp:Shirayev:1996, | |
| author = {Larry Shepp and Albert Shiryaev}, | |
| title = {Hiring and Firing Optimally in a Large Corporation}, | |
| journal = {Journal of Economic Dynamics and Control}, | |
| publisher = {Kluwer Academic Publishers-Plenum Publishers}, | |
| volume = {20}, | |
| number = {9-10}, | |
| year = {1996}, | |
| pages = {1523--1539}, | |
| abstract = {We give a simple stochastic model for the optimal size of staff of a large (especially, but not only, research) corporation as a function of its wealth and provide a quantitative theory with explicit prescriptions for increasing, decreasing or leaving constant the number of personnel in order to maximize total profit, discounted with fixed interest rate. Features of the optimal policy seem in at least qualitative agreement with observed practice in that, for example, there are occasional large-scale downsizings similar to large layoffs or incentive retirement plans observed in real corporations. In the optimal plan, this type of firing occurs only on an upswing, i.e., when the company's fortune ascends to a threshold relative to staff size. Small-scale or ‘attrition’ firing also occurs under the optimal policy, but this type of firing occurs only on a downswing, when the company's fortune descends to a threshold relative to staff size. The model is extremely simple and depends on only five estimable parameters; thus it should be useful for guiding or, at the least, stimulating thought about corporate sizing policy).} | |
| } | |
| @Article{Shilony:1985, | |
| author = {Shilony, Y.}, | |
| title = {The Sequence Method for Finding Solutions to Infinite Games: A First Demonstrating Example}, | |
| journal = {Journal of Optimization Theory and Applications}, | |
| publisher = {Kluwer Academic Publishers-Plenum Publishers}, | |
| volume = {46}, | |
| number = {1}, | |
| year = {1985}, | |
| pages = {105--117} | |
| } | |
| @Article{Shmaya:Solan:2004, | |
| author = {Shmaya, Eran and Solan, Eilon}, | |
| title = {Two-Player Non-Zero-Sum Stopping Games in Discrete Time}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {32}, | |
| number = {3B}, | |
| year = {2004}, | |
| month = {July}, | |
| pages = {2733--2764} | |
| } | |
| @Article{Siegmund:1967, | |
| author = {Siegmund, David Oliver}, | |
| title = {Some Problems in the Theory of Optimal Stopping Rules}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {38}, | |
| number = {6}, | |
| year = {1967}, | |
| month = {June}, | |
| pages = {1627--1640} | |
| } | |
| @Article{Siegmund:1982, | |
| author = {Siegmund, David Oliver}, | |
| title = {A Sequential Confidence Interval for the Odds Ratio}, | |
| journal = {Probability and Mathematical Statistics}, | |
| volume = {2}, | |
| number = {2}, | |
| year = {1982}, | |
| pages = {149--156} | |
| } | |
| @Article{Siegmund:1986, | |
| author = {Siegmund, David Oliver}, | |
| title = {Boundary Crossing Probabilities and Statistical Applications}, | |
| journal = {The Annals of Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {14}, | |
| number = {2}, | |
| year = {1986}, | |
| month = {June}, | |
| pages = {361--404} | |
| } | |
| @Article{Siegmund:1988, | |
| author = {Siegmund, David Oliver}, | |
| title = {Approximate Tail Probabilities for the Maxima of Some Random Fields}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {16}, | |
| number = {2}, | |
| year = {1988}, | |
| month = {April}, | |
| pages = {487--501} | |
| } | |
| @Article{Siegmund:2003, | |
| author = {Siegmund, David Oliver}, | |
| title = {Herbert Robbins and Sequential Analysis}, | |
| journal = {The Annals of Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {31}, | |
| number = {2}, | |
| year = {1995}, | |
| month = {April}, | |
| pages = {255--271} | |
| } | |
| @Article{Siegmund:Venkatraman:1995, | |
| author = {Siegmund, David and Venkatraman, E. S.}, | |
| title = {Using the Generalized Likelihood Ratio Statistic for Sequential Detection of a Change-Point}, | |
| journal = {The Annals of Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {23}, | |
| number = {1}, | |
| year = {1995}, | |
| month = {February}, | |
| pages = {255--271} | |
| } | |
| @Article{Siegmund:Yakir:2000a, | |
| author = {Siegmund, David and Yakir, Benjamin}, | |
| title = {Approximate $p$-values for Local Sequence Alignments}, | |
| journal = {The Annals of Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {28}, | |
| number = {3}, | |
| year = {2000}, | |
| month = {May}, | |
| pages = {657--680} | |
| } | |
| @Article{Siegmund:Yakir:2000b, | |
| author = {Siegmund, David and Yakir, Benjamin}, | |
| title = {Tail Probabilities for the Null Distribution of Scanning Statistics}, | |
| journal = {{B}ernoulli}, | |
| publisher = {{B}ernoulli Society for Mathematical Statistics and Probability}, | |
| volume = {6}, | |
| number = {2}, | |
| year = {2000}, | |
| month = {April}, | |
| pages = {191--213} | |
| } | |
| @Article{Simon:2007, | |
| author = {Simon, Robert Samuel}, | |
| title = {The Structure of Non-Zero-Sum Stochastic Games}, | |
| journal = {Advances in Applied Mathematics}, | |
| volume = {38}, | |
| year = {2007}, | |
| pages = {1--26} | |
| } | |
| @Article{Smith:1975, | |
| author = {Smith, M.H.}, | |
| title = {A Secretary Problem with Uncertain Employment}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {12}, | |
| number = {3}, | |
| year = {1975}, | |
| month = {September}, | |
| pages = {620--624} | |
| } | |
| @Article{Smith:Deely:1975, | |
| author = {Smith, M.H. and Deely, J. J.}, | |
| title = {A Secretary Problem with Finite Memory}, | |
| journal = {Journal of the American Statistical Association}, | |
| volume = {70}, | |
| number = {350}, | |
| year = {1975}, | |
| month = {June}, | |
| pages = {357--361} | |
| } | |
| @Article{Solan:1999, | |
| author = {Solan, Eilon}, | |
| title = {Three-Player Absorbing Games}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {24}, | |
| number = {3}, | |
| year = {1999}, | |
| month = {August}, | |
| pages = {669--698}, | |
| abstract = {An n-player absorbing game is an n-player stochastic game where all the states but one are absorbing (a state is absorbing if once it is reached, the probability to leave it is zero, whatever the players play). We prove that every three-player absorbing game has an undiscounted equilibrium payoff.} | |
| } | |
| @Article{Solan:Vieille:2001, | |
| author = {Solan, Eilon and Vieille, Nicolas}, | |
| title = {Quitting Games}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {26}, | |
| number = {2}, | |
| year = {2001}, | |
| pages = {265-285} | |
| } | |
| @Article{Solan:Vieille:2002, | |
| author = {Solan, Eilon and Vieille, Nicolas}, | |
| title = {Correlated Equilibrium in Stochastic Games}, | |
| journal = {Games and Economic Behavior}, | |
| volume = {38}, | |
| year = {2002}, | |
| pages = {362-399} | |
| } | |
| @Article{Solan:Vieille:2003, | |
| author = {Solan, Eilon and Vieille, Nicolas}, | |
| title = {Deterministic Multi-Player {D}ynkin Games}, | |
| journal = {Journal of Mathematical Economics}, | |
| volume = {1097}, | |
| year = {2003}, | |
| pages = {1-19} | |
| } | |
| @Incollection{Solan:Vieille:2004, | |
| author = {Solan, Eilon and Vieille, Nicolas}, | |
| title = {Stopping Games - Recent Results}, | |
| booktitle = {Advances in Dynamic Games}, | |
| editor = {Nowak, Andrzej S. and Szajowski, Krzysztof}, | |
| series = {Annals of the International Society of Dynamic Games}, | |
| publisher = {Birkhauser Boston}, | |
| volume = {7}, | |
| year = {2004}, | |
| pages = {221--231}, | |
| abstract = {We survey recent results on the existence of the value in zero- sum stopping games with discrete and continuous time, and on the existence of $\epsilon$-equilibria in non zero-sum games with discrete time.} | |
| } | |
| @Article{Sonin:1976, | |
| author = {Sonin, I. M.}, | |
| title = {Game Problems Connected with Best Choice}, | |
| journal = {Cybernetics}, | |
| publisher = {Kluwer Academic Publishers-Plenum Publishers}, | |
| volume = {12}, | |
| number = {2}, | |
| year = {1976}, | |
| pages = {246--251} | |
| } | |
| @Article{Stadje:1985a, | |
| author = {Stadje, Wolfgang}, | |
| title = {Estimation Problems for Samples with Measurement Errors}, | |
| journal = {The Annals of Statistics}, | |
| volume = {13}, | |
| number = {4}, | |
| year = {1985}, | |
| pages = {1592-1615} | |
| } | |
| @Article{Stadje:1985b, | |
| author = {Stadje, Wolfgang}, | |
| title = {On Multiple Stopping Rules}, | |
| journal = {Optimization}, | |
| volume = {16}, | |
| year = {1985}, | |
| pages = {401-418} | |
| } | |
| @Article{Stadje:1987a, | |
| author = {Stadje, Wolfgang}, | |
| title = {An Optimal Stopping Problem with Finite Horizon for Sums of I.I.D. Random Variables}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {26}, | |
| number = {}, | |
| year = {1987}, | |
| pages = {107-121} | |
| } | |
| @Incollection{Stadje:1987b, | |
| author = {Stadje, Wolfgang}, | |
| title = {An Optimal k-Stopping Problem for the Poisson Process}, | |
| booktitle = {Mathematical Statistics and Probability Theory}, | |
| editor = {Bauer, P. and Konecny, F. and Wertz, W.}, | |
| publisher = {Springer Netherlands}, | |
| year = {1987}, | |
| pages = {231-244} | |
| } | |
| @Article{Stadje:1997, | |
| author = {Stadje, Wolfgang}, | |
| title = {An Optimal Stopping Problem with Two Levels of Incomplete Information}, | |
| journal = {Mathematical Methods of Operations Research}, | |
| volume = {55}, | |
| number = {}, | |
| year = {1997}, | |
| pages = {119-131} | |
| } | |
| @Article{Stadje:2008, | |
| author = {Stadje, Wolfgang}, | |
| title = {The Maximum Average Gain in a Sequence of {B}ernoulli Games}, | |
| journal = {The American Mathematical Monthly}, | |
| volume = {115}, | |
| number = {10}, | |
| year = {2008}, | |
| pages = {902-910} | |
| } | |
| @Article{Starr:1972, | |
| author = {Starr, Norman}, | |
| title = {How to Win a War if You Must: Optimal Stopping Based on Success Runs}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| month = {December}, | |
| volume = {43}, | |
| number = {6}, | |
| year = {1972}, | |
| pages = {1884--1893} | |
| } | |
| @Article{Stein:Seale:Rapoport:2003, | |
| author = {Stein, William E. and Seale, Darryl A. and Rapoport, Amnon}, | |
| title = {Analysis of Heuristic Solutions to the Best Choice Problem}, | |
| journal = {European Journal of Operational Research}, | |
| volume = {151}, | |
| number = {1}, | |
| year = {2003}, | |
| pages = {140-152}, | |
| abstract = {In the sequential decision making task known as the best choice problem, n items are presented in a random order one at a time. After each item, the decision maker (DM) can determine only their relative ranks. The DM's goal is to select the best of all n items without the possibility of recalling previously observed items. The purpose of this paper is to compare the optimal policy to three classes of heuristic decision rules that were identified and studied in previous research. We also investigate the limiting case as $n\rightarrow\infty$.} | |
| } | |
| @Article{Stewart:1978, | |
| author = {Stewart, Teodor J.}, | |
| title = {Optimal Selection from a Random Sequence with Learning of the Underlying Distribution}, | |
| journal = {Journal of the American Statistical Association}, | |
| volume = {73}, | |
| number = {364}, | |
| year = {1978}, | |
| month = {December}, | |
| pages = {775--780} | |
| } | |
| @Article{Stewart:1981, | |
| author = {Stewart, Theodor J.}, | |
| title = {The Secretary Problem with an Unknown Number of Options}, | |
| journal = {Operations Research}, | |
| volume = {29}, | |
| number = {1}, | |
| year = {1981}, | |
| month = {January-February}, | |
| pages = {130--145} | |
| } | |
| @Article{Stout:Chow:1969, | |
| author = {Stout, William F. and Chow, Yuan Shih}, | |
| title = {On the Expected Value of a Stopped Stochastic Sequence}, | |
| journal = {The Annals of Mathematical Statistics}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {40}, | |
| number = {2}, | |
| year = {1969}, | |
| month = {April}, | |
| pages = {456--461} | |
| } | |
| @Article{Suchwalko:Szajowski:2002, | |
| author = {Suchwalko, Artur and Szajowski, Krzysztof}, | |
| title = {Non Standard No Information Secretary Problems}, | |
| journal = {Scientiae Mathematicae Japonicae Online}, | |
| volume = {6}, | |
| year = {2002}, | |
| pages = {423--436} | |
| } | |
| @Incollection{Suchwalko:Szajowski:2003, | |
| author = {Suchwalko, Artur and Szajowski, Krzysztof}, | |
| title = {On Bruss' Stopping Problem with General Gain Function}, | |
| booktitle = {Optimal Stopping and Stochastic Games}, | |
| publisher = {NA}, | |
| year = {2003}, | |
| pages = {161--171} | |
| } | |
| @Article{Szajowski:1992, | |
| author = {Szajowski, Krzysztof}, | |
| title = {On non-zero sum game with priority in the secretary problem}, | |
| journal = {Mathematica Japonica}, | |
| volume = {37}, | |
| number = {3}, | |
| year = {1992}, | |
| pages = {415--426} | |
| } | |
| @Article{Szajowski:1993, | |
| author = {Szajowski, Krzysztof}, | |
| title = {Double Stopping by Two Decision Makers}, | |
| journal = {Advanced Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {25}, | |
| number = {}, | |
| year = {1993}, | |
| pages = {438-452} | |
| } | |
| @Article{Szajowski:1994, | |
| author = {Szajowski, Krzysztof}, | |
| title = {{M}arkov Stopping Games with Random Priority}, | |
| journal = {Zeitschrift für Operations Research}, | |
| publisher = {Physica-Verlag}, | |
| volume = {39}, | |
| number = {1}, | |
| year = {1994}, | |
| pages = {69-84} | |
| } | |
| @Article{Szajowski:1995, | |
| author = {Szajowski, Krzysztof}, | |
| title = {Optimal Stopping of a Discrete {M}arkov Process by Two Decision Makers}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| publisher = {Society for Industrial and Applied Mathematics}, | |
| volume = {33}, | |
| number = {5}, | |
| year = {1995}, | |
| pages = {1392--1410} | |
| } | |
| @Article{Szajowski:2007, | |
| author = {Szajowski, Krzysztof}, | |
| title = {A Game Version of the Cowan-Zabczyk-Bruss' Problem}, | |
| journal = {Statistics and Probability Letters}, | |
| publisher = {Elsevier Sciences Ltd}, | |
| volume = {77}, | |
| year = {2007}, | |
| pages = {1683--1689} | |
| } | |
| @Article{Szajowski:2009, | |
| author = {Szajowski, Krzysztof}, | |
| title = {A Rank-Based Selection with Cardinal Payoffs and a Cost of Choice}, | |
| journal = {Scientiae Mathematicae Japonicae Online}, | |
| year = {2009}, | |
| pages = {69--77} | |
| } | |
| @Article{Szajowski:2011, | |
| author = {Szajowski, Krzysztof}, | |
| title = {On a Random Number of Disorders}, | |
| journal = {Probability and Mathematical Statistics}, | |
| volume = {31}, | |
| number = {1}, | |
| year = {2011}, | |
| pages = {17-45} | |
| } | |
| @Incollection{Szajowski:Yasuda:1997, | |
| author = {Szajowski, Krzysztof and Yasuda, Masami}, | |
| title = {Voting Procedure on Stopping Games of {M}arkov Chain}, | |
| booktitle = {Stochastic Modelling in Innovative Manufacturing}, | |
| series = {Lecture Notes in Economics and Mathematical Systems}, | |
| editor = {Christer, Anthony H. and Osaki, Shunji and Thomas, Lyn C.}, | |
| publisher = {Springer Berlin Heidelberg}, | |
| volume = {445}, | |
| year = {1997}, | |
| pages = {68-80} | |
| } | |
| @Article{Tamaki:1979a, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Recognizing Both the Maximum and the Second Maximum of a Sequence}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {16}, | |
| number = {}, | |
| year = {1979}, | |
| pages = {803-812} | |
| } | |
| @Article{Tamaki:1979b, | |
| author = {Tamaki, Mitsushi}, | |
| title = {A Secretary Problem with Double Choices}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {22}, | |
| number = {4}, | |
| year = {1979}, | |
| month = {December}, | |
| pages = {257--264} | |
| } | |
| @Article{Tamaki:1984, | |
| author = {Tamaki, Mitsushi}, | |
| title = {The Secretary Problem with Optimal Assignment}, | |
| journal = {Operations Research}, | |
| volume = {32}, | |
| number = {4}, | |
| year = {1984}, | |
| month = {July-August}, | |
| pages = {847--858} | |
| } | |
| @Article{Tamaki:1986, | |
| author = {Tamaki, Mitsushi}, | |
| title = {A Generalized Problem of Optimal Selection and Assignment}, | |
| journal = {Operations Research}, | |
| volume = {34}, | |
| number = {3}, | |
| year = {1986}, | |
| month = {May-June}, | |
| pages = {486--493} | |
| } | |
| @Article{Tamaki:1988, | |
| author = {Tamaki, Mitsushi}, | |
| title = {A Bayesian Approach to the Best-Choice Problem}, | |
| journal = {Journal of the American Statistical Association}, | |
| volume = {83}, | |
| number = {404}, | |
| year = {1988}, | |
| month = {December}, | |
| pages = {1129--1133} | |
| } | |
| @Article{Tamaki:1991, | |
| author = {Tamaki, Mitsushi}, | |
| title = {A Secretary Problem with Uncertain Employment and Best Choice of Available Candidates}, | |
| journal = {Operations Research}, | |
| volume = {39}, | |
| number = {2}, | |
| year = {1991}, | |
| month = {March-April}, | |
| pages = {274--284} | |
| } | |
| @Incollection{Tamaki:2000, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Minimal Expected Ranks for the Secretary Problems with Uncertain Selection}, | |
| booktitle = {Game Theory, Optimal Stopping, Probability and Statistics}, | |
| editor = {Bruss, F. Thomas and Le Cam, Lucien}, | |
| publisher = {Institute of Mathematical Statistics}, | |
| series = {Lecture Notes--Monograph Series}, | |
| volume = {35}, | |
| year = {2000}, | |
| pages = {127--139} | |
| } | |
| @Article{Tamaki:2001, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Optimal Stopping On Trajectories and the Ballot Problem}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {38}, | |
| year = {2001}, | |
| pages = {946--959} | |
| } | |
| @Article{Tamaki:2007, | |
| author = {Tamaki, Mitsushi}, | |
| title = {A Note on the Stewart's Secretary Problem}, | |
| journal = {Departmental Bulletin Paper}, | |
| volume = {Kyoto University Research Information Repository}, | |
| year = {2007}, | |
| pages = {116--121} | |
| } | |
| @Article{Tamaki:2009, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Optimal Choice of the Best Available Applicant in Full Information Models}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {46}, | |
| year = {2009}, | |
| pages = {1086--1099} | |
| } | |
| @Article{Tamaki:2010, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Sum the Multiplicative Odds to One And Stop}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {47}, | |
| number = {3}, | |
| year = {2010}, | |
| month = {September}, | |
| pages = {761--777}, | |
| abstract = {We consider the optimal stopping problem of maximizing the probability of stopping on any of the last $m$ successes of a sequence of independent Bernoulli trials of length $n$, where $m$ and n are predetermined integers such that $1 \leq m < n$. The optimal stopping rule of this problem has a nice interpretation, that is, it stops on the first success for which the sum of the m-fold multiplicative odds of success for the future trials is less than or equal to 1. This result can be viewed as a generalization of Bruss' (2000) odds theorem. Application will be made to the secretary problem. For more generality, we extend the problem in several directions in the same manner that Ferguson (2008) used to extend the odds theorem. We apply this extended result to the full-information analogue of the secretary problem, and derive the optimal stopping rule and the probability of win explicitly. The asymptotic results, as $n$ tends to $\infty$, are also obtained via the planar Poisson process approach.} | |
| } | |
| @Article{Tamaki:2011, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Maximizing }, | |
| journal = {Advanced Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {43}, | |
| number = {3}, | |
| year = {2011}, | |
| pages = {760--781} | |
| } | |
| @Article{Tamaki:2013, | |
| author = {Tamaki, Mitsushi}, | |
| title = {Optimal Stopping Rule for the No-Information Duration Problem with Random Horizon}, | |
| journal = {Advanced Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {45}, | |
| number = {4}, | |
| year = {2013}, | |
| pages = {1028--1048} | |
| } | |
| @Article{Tamaki:Ohno:2000, | |
| author = {Tamaki, Mitsushi and Ohno, Katsuhisa}, | |
| title = {On a Generalization of the Secretary Problem with Uncertain Selection}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {43}, | |
| number = {1}, | |
| year = {2000}, | |
| month = {March}, | |
| pages = {219--243} | |
| } | |
| @Techreport{Tamaki:Pearce:Szajowski:2002, | |
| author = {Tamaki, Mitsushi and Pearce, Charles E. M. and Szajowski, Krzysztof}, | |
| title = {Multiple Choice Problems Related to the Duration of the Secretary Problem}, | |
| institution = {NA}, | |
| year = {2002} | |
| } | |
| @Incollection{Tamaki:Wang:2010, | |
| author = {Tamaki, Mitsushi and Wang, Qi}, | |
| title = {A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals}, | |
| booktitle = {Optimization and Optimal Control}, | |
| editor = {Chinchuluun, A. and Pardalos, P.M. and Enkhbat, R. and Tseveendorj}, | |
| series = {Optimization and Its Applications 39}, | |
| publisher = {Springer}, | |
| year = {2010}, | |
| pages = {499--510} | |
| } | |
| @Article{Touzi:Vieille:2002, | |
| author = {Touzi, Nizar and Vieille, Nicolas}, | |
| title = {Continuous-Time {D}ynkin Games with Mixed Strategies}, | |
| journal = {{S}{I}{A}{M} Journal on Control and Optimization}, | |
| volume = {41}, | |
| number = {4}, | |
| year = {2002}, | |
| pages = {1073-1088} | |
| } | |
| @Article{Lawler:Vanderbei:1983, | |
| author = {Lawler, G. F. and Vanderbei, Robert J.}, | |
| title = {{M}arkov Strategies for Optimal Control Problems Indexed by a Partially Ordered Set}, | |
| journal = {The Annals of Probability}, | |
| publisher = {The Institute of Mathematical Statistics}, | |
| volume = {11}, | |
| number = {3}, | |
| year = {1983}, | |
| month = {August}, | |
| pages = {642-647} | |
| } | |
| @Article{Vanderbei:1980, | |
| author = {Vanderbei, Robert J.}, | |
| title = {The Optimal Choice of a Subset of a Population}, | |
| journal = {Mathematics of Operations Research}, | |
| publisher = {The Institute of Management Science and the Operations Research Society of America}, | |
| volume = {5}, | |
| number = {4}, | |
| year = {1980}, | |
| month = {November}, | |
| pages = {481-486}, | |
| abstract = {We check a ranked population in random order. At each step we either accept or reject the observed sample. As a result we get a partition of the population into two parts: accepted and rejected. We are interested only in the case when all accepted samples are better than all rejected. Under this condition, we maximize the probability to obtain a fixed size $k$ of the accepted part. An arbitrary gain function is also considered.} | |
| } | |
| @Article{Sardelis:Valahas:1999, | |
| author = {Sardelis, Dimitris A. and Valahas, Theodoros M.}, | |
| title = {Decision Making: A Golden Rule}, | |
| journal = {The American Mathematical Monthly}, | |
| publisher = {Mathematical Association of America}, | |
| volume = {106}, | |
| number = {3}, | |
| year = {1999}, | |
| month = {March}, | |
| pages = {215-226} | |
| } | |
| @Article{Villareal:Karwan:1981a, | |
| author = {Villarreal, Bernardo and Karwan, Mark H.}, | |
| title = {Multicriteria Integer Programming: A (Hybrid) Dynamic Programming Recursive Approach}, | |
| journal = {Mathematical Programming}, | |
| publisher = {Springer-Verlag}, | |
| volume = {21}, | |
| number = {1}, | |
| year = {1981}, | |
| pages = {204-223} | |
| } | |
| @Article{Villareal:Karwan:1981b, | |
| author = {Villarreal, Bernardo and Karwan, Mark H.}, | |
| title = {An Interactive Dynamic Programming Approach to Multicriteria Discrete Programming}, | |
| journal = {Journal of Mathematical Analysis and Applications}, | |
| publisher = {Elsevier Sciences Ltd}, | |
| volume = {81}, | |
| number = {2}, | |
| year = {1981}, | |
| pages = {524--544}, | |
| abstract = {Several interactive schemes for solving multicriteria discrete programming problems are developed under a dynamic programming framework. It is assumed that the decision maker's preference structure satisfies the conditions of transitivity, monotonicity, and nonsatiation. Hybrid procedures are also structured by including branch and bound ideas into the recursions. Initial computational results are offered.} | |
| } | |
| @Article{Villareal:Karwan:1982, | |
| author = {Villarreal, Bernardo and Karwan, Mark H.}, | |
| title = {Multicriteria Dynamic Programming with an Application to the Integer Case}, | |
| journal = {Journal of Optimization Theory and Applications}, | |
| publisher = {Kluwer Academic Publishers-Plenum Publishers}, | |
| volume = {38}, | |
| number = {1}, | |
| year = {1982}, | |
| pages = {43-69} | |
| } | |
| @Article{Wang:Wang:Liu:2008, | |
| author = {Wang, Yuan and Wang, Kan-liang and Liu, Qin-shun}, | |
| title = {Extension on Cut-off Rules of Sequential Observation and Selection Problem}, | |
| journal = {Systems Engineering - Theory and Practice}, | |
| publisher = {Blackwell Publishing for the American Finance Association}, | |
| volume = {28}, | |
| number = {2}, | |
| year = {2008}, | |
| pages = {74--81}, | |
| abstract = {Cut-off rules specialized in sequential observation and selection problems (SOSP). A class of \{SOSP\} was studied, in which a decision maker (DM) face multi-times selection case with the objective of minimizing the average rank of all selected alternatives. In modeling this class of problems, the article firstly present the optimal cut-off rules that use maximum, before cut-off, as benchmark, and then report results from simulation experiment. Furthermore, the article proposes that to fall benchmark is more efficient than to decrease cut-off value for improving the average payoff. Thus, the optimal cut-off rule was revised by replacing their maximum benchmark with average benchmark based on the risk aversion and extreme aversion. The results from simulation experiment indicate that the revised cut-off rule has better average payoffs. At last, a proof process that the 20 percent is the approximate optimal ratio to estimate the benchmark brings this article into a close.} | |
| } | |
| @Article{Welch:1991, | |
| author = {Welch, Ivo}, | |
| title = {Sequential Sales, Learning, and Cascades}, | |
| journal = {The Journal of Finance}, | |
| publisher = {Blackwell Publishing for the American Finance Association}, | |
| volume = {47}, | |
| number = {2}, | |
| year = {1992}, | |
| month = {June}, | |
| pages = {695--732} | |
| } | |
| @Article{Wilson:1991, | |
| author = {Wilson, John G.}, | |
| title = {Optimal Choice and Assignment of the Best $m$ of $n$ Randomly Arriving Items}, | |
| journal = {Stochastic Processes and their Applications}, | |
| volume = {39}, | |
| number = {2}, | |
| year = {1991}, | |
| pages = {325--343}, | |
| abstract = {A total of $n$ items arrive at random. The decision maker must either select or discard the current item. Ranks must be assigned to items as they are selected. The decision maker's goal is to follow a procedure that maximises the probability of selecting the m best items and assigning them according to their rank order. For $m=1$ this is the classical secretary problem. Rose (1982) solved the $m=2$ case. Key mathematical properties for the general m out of n problem are developed: functional equations expressing the general problem in terms of lower dimensional problems and theorems regarding the structure of optimal strategies are provided. A key optimal stopping result for the general problem is provided. Using these results a procedure for solving the above problem for any given m and n is developed. Using this algorithm, explicit formulas -- similar in form to those for the well known m=1 and $m=2$ cases -- can be derived. As an example, explicit formulas for the previously unsolved $m=3$ finite secretary problem are provided.} | |
| } | |
| @Article{Yang:1982, | |
| author = {Yang, Hwa-Ming}, | |
| title = {Optimal Selection of the $T$ Best of a Sequence with Sampling Cost}, | |
| journal = {Naval Research Logistics (NRL)}, | |
| publisher = {Wiley Subscription Services, Inc., A Wiley Company}, | |
| volume = {34}, | |
| number = {2}, | |
| year = {1987}, | |
| pages = {281--292} | |
| } | |
| @Article{Yang:1974, | |
| author = {Yang, Mark C. K.}, | |
| title = {Recognizing the Maximum of a Random Sequence Based on Relative Rank with Backward Solicitation}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {11}, | |
| number = {3}, | |
| month = {September}, | |
| year = {1974}, | |
| pages = {504--512}, | |
| abstract = {The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.} | |
| } | |
| @Article{Yang:2009, | |
| author = {Yang, Jiing-Ru}, | |
| title = {Selecting the Last Record with Recall in a Sequence of Independent {B}ernoulli Trials}, | |
| journal = {Statistica Sinica}, | |
| volume = {19}, | |
| year = {2009}, | |
| pages = {355--361} | |
| } | |
| @Article{Yao:1997, | |
| author = {Yao, Yi-Ching}, | |
| title = {On Independence of k-Record Processes: Ignatov's Theorem Revisited}, | |
| journal = {The Annals of Probability}, | |
| volume = {7}, | |
| number = {3}, | |
| year = {1997}, | |
| pages = {815-821}, | |
| abstract = {For an infinite sequence of independent and identically distributed (i.i.d.) random variables, the $k$-record process consists of those terms that are the $k$th largest at their appearance. Ignatov's theorem states that the $k$-record processes, $k = 1, 2, ..., $ are i.i.d. A new proof is given which is based on a ``continualization'' argument. An advantage of this fairly simple approach is that Ignatov's theorem can be stated in a more general form by allowing for different tiebreaking rules. In particular, three tiebreakers are considered and shown to be related to Bernoulli, geometric and Poisson distributions.} | |
| } | |
| @Article{Yasuda:1984a, | |
| author = {Yasuda, Masami}, | |
| title = {Asymptotic Results for the Best-Choice Problem with a Random Number of Objects}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {21}, | |
| number = {}, | |
| year = {1984}, | |
| pages = {521--536} | |
| } | |
| @Article{Yasuda:1984b, | |
| author = {Yasuda, Masami}, | |
| title = {On the Optimal Stopping Problem of {M}arkov Chains with Variational Inequalities}, | |
| journal = {Journal of the College of Arts and Sciences, Chiba University}, | |
| volume = {B-17}, | |
| year = {1984}, | |
| month = {November}, | |
| pages = {11--16} | |
| } | |
| @Article{Yasuda:1985, | |
| author = {Yasuda, Masami}, | |
| title = {On a Randomized Strategy in {N}eveu's Stopping Problem}, | |
| journal = {Stochastic Processes and their Applications}, | |
| publisher = {North-Holland}, | |
| volume = {21}, | |
| year = {1985}, | |
| pages = {159--166} | |
| } | |
| @Article{Yasuda:1988a, | |
| author = {Yasuda, Masami}, | |
| title = {The Optimal Value of {M}arkov Stopping Problems with One-Step Look Ahead Policy}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {25}, | |
| number = {3}, | |
| year = {1988}, | |
| pages = {544--552}, | |
| abstract = {This paper treats stopping problems on Markov chains in which the OLA (one-step look ahead) policy is optimal. Its associated optimal value can be explicitly expressed by a potential for a charge function of the difference between the immediate reward and the one-step-after reward. As an application to the best choice problem, we shall obtain the value of three problems: the classical secretary problem, a problem with a refusal probability and a problem with a random number of objects.} | |
| } | |
| @Incollection{Yasuda:1988b, | |
| author = {Yasuda, Masami}, | |
| title = {On the Value for OLA-Optimal Stopping Problem by Potential Theoretic Method}, | |
| booktitle = {Probability Theory and Mathematical Statistics}, | |
| editor = {Watanabe, S. and Prokhorov, Yu V.}, | |
| publisher = {Springer-Verlag, Berlin}, | |
| year = {1988}, | |
| pages = {571--580} | |
| } | |
| @Article{Yasuda:1995, | |
| author = {Yasuda, Masami}, | |
| title = {Explicit Optimal Value for {D}ynkin's Stopping Game}, | |
| journal = {Mathematical and Computer Modelling}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {22}, | |
| number = {10-12}, | |
| year = {1995}, | |
| pages = {313--324}, | |
| abstract = {Under the One-step Look Ahead rule of Dynamic Programming, an explicit game value of Dynkin's stopping problem for a Markov chain is obtained by using a potential operator. The condition on the One-step rule could be extended to the $k$-step and infinity-step rule. We shall also decompose the game value as the sum of two explicit functions under these rules.} | |
| } | |
| @Article{Yasuda:Nakagami:Kurano:1982, | |
| author = {Yasuda, Masami and Nakagami, Junichi and Kurano, Masami}, | |
| title = {Multi-Variate Stopping Problems with a Monotone Rule}, | |
| journal = {Journal of the Operations Research Society of {J}apan}, | |
| volume = {25}, | |
| number = {4}, | |
| year = {1982}, | |
| month = {December}, | |
| pages = {334-349} | |
| } | |
| @Article{Yeo:1998, | |
| author = {Yeo, Geoffrey F.}, | |
| title = {Interview Costs in the Secretary Problem}, | |
| journal = {Australian and New Zealand Journal of Statistics}, | |
| publisher = {Blackwell Publishers Ltd}, | |
| volume = {40}, | |
| number = {2}, | |
| year = {1998}, | |
| pages = {215--219} | |
| } | |
| @Article{Yoshida:Yasuda:Nakagami:Kurano:2000, | |
| author = {Yoshida, Y. and Yasuda, Masami and Nakagami, Junichi and Kurano, Masami}, | |
| title = {Optimal Stopping Problems in a Stochastic and Fuzzy System}, | |
| journal = {Journal of Mathematical Analysis and Applications}, | |
| volume = {246}, | |
| year = {2000}, | |
| pages = {135-149} | |
| } | |
| @Article{Zuckerman:1986, | |
| author = {Zuckerman, Dror}, | |
| title = {Optimal Stopping in a Continuous Search Model}, | |
| journal = {Journal of Applied Probability}, | |
| publisher = {Applied Probability Trust}, | |
| volume = {23}, | |
| number = {2}, | |
| year = {1986}, | |
| pages = {514--518}, | |
| abstract = {We examine a continuous search model in which rewards (e.g. job offers in a search model in the labor market, price offers for a given asset, etc.) are received randomly according to a renewal process determined by a known distribution function. The rewards are non-negative independent and have a common distribution with finite mean. Over the search period there is a constant cost per unit time. The searcher's objective is to choose a stopping time at which he receives the highest available reward (offer), so as to maximize the net expected discounted return. If the interarrival time distribution in the renewal process is New Better than Used (NBU), it is shown that the optimal stopping strategy possesses the control limit property. The term `control limit policy' refers to a strategy in which we accept the first reward (offer) which exceeds a critical control level.} | |
| } | |
| @Article{Zwick:Rapoport:1985, | |
| author = {Zwick, Rami and Rapoport, Amnon}, | |
| title = {Relative Gain Maximization in Sequential 3-Person Characteristic Function Games}, | |
| journal = {Journal of Mathematical Psychology}, | |
| volume = {29}, | |
| year = {1985}, | |
| pages = {333--359}, | |
| %%% BOOKS | |
| @Book{Ghosh:Sen:1991:book, | |
| title = {Handbook of Sequential Analysis}, | |
| editor = {Ghosh, Bhaskar Kumar and Sen, Pranab Kumar}, | |
| series = {Statistics, Textbooks and Monographs}, | |
| publisher = {CRC Press}, | |
| year = {1991} | |
| } | |
| @Book{Neveu:1975:book, | |
| author = {Neveu, Jacques}, | |
| title = {Discrete-Parameter Martingales}, | |
| publisher = {North-Halland Publishing Company}, | |
| year = {1975} | |
| } | |
| @Book{ | |
| 1992:book, | |
| author = {Ferguson, Thomas}, | |
| title = {Optimal Stopping And Applications}, | |
| publisher = {Available online: {http://www.math.ucla.edu/~tom/Stopping/Contents.html}}, | |
| year = {1992} | |
| } | |
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| \documentclass[12pt]{article} | |
| \usepackage[a4paper,centering]{geometry} | |
| %\renewcommand{\baselinestretch}{1.5}%control spacing | |
| \usepackage[T1]{fontenc} | |
| \usepackage[utf8]{inputenc} | |
| \usepackage{lmodern} | |
| \usepackage[english]{babel} | |
| \usepackage{times,mathptmx} | |
| \usepackage[scaled=0.92]{helvet}% 92% is suitable with Times | |
| \usepackage{amsmath,amsfonts,amssymb} | |
| \usepackage{natbib} | |
| \bibliographystyle{plain} %plain | |
| \usepackage{bibtopic} | |
| \renewcommand{\thebtauxfile}{bt\arabic{btauxfile}} | |
| %Use: \btPrintCited%\btPrintNotCited%\btPrintAll | |
| \input{ReferencesSecretaryProblem} |
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| \begin{document} | |
| \section{Surveys on the Secretary Problem} | |
| \begin{btUnit} | |
| \begin{btSect}{BibSecretaryProblem} | |
| \nocite{Abdelaziz:Krichen:2007} | |
| \nocite{Ferguson:1989} | |
| \nocite{Freeman:1983} | |
| \nocite{Gilbert:Mosteller:1966} | |
| \nocite{Hill:Kertz:1992} | |
| \nocite{Preater:1998} | |
| \nocite{Sardelis:Valahas:1999} | |
| \btPrintCited | |
| \end{btSect} | |
| \end{btUnit} | |
| \section{Books on the Secretary Problem} | |
| \begin{btUnit} | |
| \begin{btSect}{BibSecretaryProblem} | |
| \nocite{Ghosh:Sen:1991:book} | |
| \nocite{Neveu:1975:book} | |
| \nocite{Ferguson:1992:book} | |
| \btPrintCited | |
| \end{btSect} | |
| \end{btUnit} | |
| \section{Many Players/Choices Secretary Problems} | |
| \begin{btUnit} | |
| \begin{btSect}{BibSecretaryProblem} | |
| \nocite{Abdelaziz:Krichen:2005} | |
| \nocite{Abdelaziz:Krichen:2007} | |
| \nocite{Ali:1998} | |
| \nocite{Alpern:Gal:Solan:1998} | |
| \nocite{Alpern:Gal:2009} | |
| \nocite{Ano:1989} | |
| \nocite{Ano:Ando:2000} | |
| \nocite{Ano:Tamaki:1992} | |
| \nocite{Ano:Tamaki:Hu:1996} | |
| \nocite{Assaf:Goldstein:SamuelCahn:1998} | |
| \nocite{Assaf:Goldstein:Samuel-Cahn:2003} | |
| \nocite{Assaf:Goldstein:SamuelCahn:2002} | |
| \nocite{Bartoszynski:Pleszczynska:1980} | |
| \nocite{Bearden:Connolly:2007} | |
| \nocite{Bearden:Murphy:2007} | |
| \nocite{Bearden:Rapoport:Murphy:2006} | |
| \nocite{Bismuth:1977} | |
| \nocite{Broder:Etc:2009} | |
| \nocite{Bruss:Louchard:1998} | |
| \nocite{Bruss:Drmota:Louchard:1998} | |
| \nocite{Bruss:Louchaurd:1998} | |
| \nocite{Chen:Rosenberg:Shepp:1997} | |
| \nocite{Chun:1996a} | |
| \nocite{Chun:1996b} | |
| \nocite{Chun:1999} | |
| \nocite{Chun:2001} | |
| \nocite{Chun:Sumichrast:2006} | |
| \nocite{Enns:Ferenstein:1985} | |
| \nocite{Enns:Ferenstein:1987} | |
| \nocite{Enns:Ferenstein:1990} | |
| \nocite{Eriksson:Sjostrand:Strimling:2007} | |
| \nocite{Eriksson:Sjostrand:Strimling:2008} | |
| \nocite{Feng:Hartman:2013} | |
| \nocite{Ferenstein:1992} | |
| \nocite{Ferenstein:2004} | |
| \nocite{Ferenstein:2005} | |
| \nocite{Ferenstein:2007} | |
| \nocite{Ferenstein:Krasnosielska:2009} | |
| \nocite{Ferguson:2004} | |
| \nocite{Ferguson:2008} | |
| \nocite{Fushimi:1981} | |
| \nocite{Glickman:2000} | |
| \nocite{Gnedin:1994} | |
| \nocite{Gnedin:Krengel:1995} | |
| \nocite{Hamadene:Hassani:2014} | |
| \nocite{Hamadene:Zhang:2010} | |
| \nocite{Kawai:Tamaki:2003} | |
| \nocite{Kennedy:Kertz:1990} | |
| \nocite{Kennedy:Kertz:1991} | |
| \nocite{Kennedy:Kertz:1992} | |
| \nocite{Nakagami:1999} | |
| \nocite{Mazalov:Falko:2008} | |
| \nocite{Porosinski:2004} | |
| \nocite{Ramsey:Cierpial:2009} | |
| \nocite{Rosenberg:Solan:Vieille:2001} | |
| \nocite{Sakaguchi:1988a} | |
| \nocite{Sakaguchi:1988b} | |
| \nocite{Sakaguchi:2004a} | |
| \nocite{Sakaguchi:2004b} | |
| \nocite{Sakaguchi:2004g} | |
| \nocite{Smith:1975} | |
| \nocite{Solan:Vieille:2004} | |
| \nocite{Zwick:Rapoport:1985} | |
| \btPrintCited | |
| \end{btSect} | |
| \end{btUnit} | |
| \section{Secretary Problems with Learning} | |
| \begin{btUnit} | |
| \begin{btSect}{BibSecretaryProblem} | |
| \nocite{Albright:1977} | |
| \nocite{Bruss:1988} | |
| \nocite{Bruss:Rogers:1991} | |
| \btPrintCited | |
| \end{btSect} | |
| \end{btUnit} | |
| \section{Secretary Problems: Everything} | |
| \begin{btUnit} | |
| \begin{btSect}{BibSecretaryProblem} | |
| \nocite{Abdelaziz:Krichen:2005} | |
| \nocite{Abdelaziz:Krichen:2007} | |
| \nocite{Albright:Derman:1972} | |
| \nocite{Albright:1974} | |
| \nocite{Albright:1977} | |
| \nocite{Ali:1998} | |
| \nocite{Alpern:Gal:Solan:1998} | |
| \nocite{Alpern:Gal:2009} | |
| \nocite{Ano:1989} | |
| \nocite{Ano:1990} | |
| \nocite{Ano:1992} | |
| \nocite{Ano:2001} | |
| \nocite{Ano:Tamaki:1992} | |
| \nocite{Ano:Tamaki:Hu:1996} | |
| \nocite{Ano:Ando:2000} | |
| \nocite{Ano:Kakinuma:Miyoshi:2010} | |
| \nocite{Arrow:Blackwell:Girshick:1949} | |
| \nocite{Assaf:Goldstein:SamuelCahn:1998} | |
| \nocite{Assaf:Goldstein:Samuel-Cahn:2003} | |
| \nocite{Assaf:Goldstein:SamuelCahn:2002} | |
| \nocite{Assaf:SamuelCahn:2002} | |
| \nocite{Baharian:Jacobson:2013} | |
| \nocite{Bai:1989} | |
| \nocite{Bajnok:Semov:2014} | |
| \nocite{Bartoszynski:Pleszczynska:1980} | |
| \nocite{Bateni:Hajiaghayi:Zadimoghaddam:2013} | |
| \nocite{Bearden:2006} | |
| \nocite{Bearden:Connolly:2007} | |
| \nocite{Bearden:Murphy:2007} | |
| \nocite{Bearden:Rapoport:Murphy:2006} | |
| \nocite{Beckmann:1990} | |
| \nocite{Bismuth:1977} | |
| \nocite{Bojdecki:1978} | |
| \nocite{Bradt:Johnson:Karlin:1956} | |
| \nocite{Broder:Etc:2009} | |
| \nocite{Bruss:1984} | |
| \nocite{Bruss:1988} | |
| \nocite{Bruss:2000} | |
| \nocite{Bruss:2003} | |
| \nocite{Bruss:2005} | |
| \nocite{Bruss:2010} | |
| \nocite{Bruss:Delbaen:2001} | |
| \nocite{Bruss:Delbaen:2004} | |
| \nocite{Bruss:Drmota:Louchard:1998} | |
| \nocite{Bruss:Ferguson:2002} | |
| \nocite{Bruss:Louchard:1998} | |
| \nocite{Bruss:Paindaveine:2000} | |
| \nocite{Bruss:Rogers:1991} | |
| \nocite{Bruss:Samuels:1987} | |
| \nocite{Bruss:Samuels:1990} | |
| \nocite{Cabilio:1977} | |
| \nocite{Campbell:Samuels:1981} | |
| \nocite{Chen:Nair:Odlyzko:Shepp:Vardi:1984} | |
| \nocite{Chen:Rosenberg:Shepp:1997} | |
| \nocite{Chen:Starr:1980} | |
| \nocite{Chow:Moriguti:Robbins:Samuels:1964} | |
| \nocite{Chow:Robbins:1961} | |
| \nocite{Chow:Robbins:1965} | |
| \nocite{Chow:Robbins:1967a} | |
| \nocite{Chow:Robbins:1967b} | |
| \nocite{Chow:Robbins:Teicher:1965} | |
| \nocite{Chudjakow:Riedel:2013} | |
| \nocite{Chun:1996a} | |
| \nocite{Chun:1996b} | |
| \nocite{Chun:1999} | |
| \nocite{Chun:2001} | |
| \nocite{Chun:Sumichrast:2006} | |
| \nocite{Cowan:Zabczyk:1978} | |
| \nocite{Darling:1986} | |
| \nocite{Das:Kamenica:2005} | |
| \nocite{David:Yechiali:1995} | |
| \nocite{Derman:Lieberman:Ross:1972} | |
| \nocite{Dhariyal:Dudewicz:1981} | |
| \nocite{Domansky:2000} | |
| \nocite{Dynkin:1962} | |
| \nocite{Dynkin:1969} | |
| \nocite{Ekstrom:Peskir:2008} | |
| \nocite{Ekstrom:Villeneuve:2006} | |
| \nocite{Elbakidze:1974} | |
| \nocite{Enns:1970a} | |
| \nocite{Enns:1970b} | |
| \nocite{Enns:Ferenstein:1985} | |
| \nocite{Enns:Ferenstein:1987} | |
| \nocite{Enns:Ferenstein:1990} | |
| \nocite{Eriksson:Sjostrand:Strimling:2007} | |
| \nocite{Eriksson:Sjostrand:Strimling:2008} | |
| \nocite{Fakeev:1968} | |
| \nocite{Feng:Hartman:2013} | |
| \nocite{Faller:Ruschendorf:2012} | |
| \nocite{Ferenstein:1992} | |
| \nocite{Ferenstein:2004} | |
| \nocite{Ferenstein:2005} | |
| \nocite{Ferenstein:2007} | |
| \nocite{Ferenstein:Krasnosielska:2009} | |
| \nocite{Ferguson:2004} | |
| \nocite{Ferguson:2008} | |
| \nocite{Ferguson:1989} | |
| \nocite{Ferguson:1992} | |
| \nocite{Frank:Samuels:1980} | |
| \nocite{Freeman:1983} | |
| \nocite{Flatau:Irle:1983} | |
| \nocite{Frank:Samuels:1980} | |
| \nocite{Frid:1968} | |
| \nocite{Fushimi:1981} | |
| \nocite{Gaver:1976} | |
| \nocite{Gianini:1977} | |
| \nocite{Gianini:Samuels:1976} | |
| \nocite{Gilbert:Mosteller:1966} | |
| \nocite{Glasser:Barron:1983} | |
| \nocite{Glickman:2000} | |
| \nocite{Gnedin:1994} | |
| \nocite{Gnedin:2004} | |
| \nocite{Gnedin:2000} | |
| \nocite{Gnedin:Sakaguchi:1992} | |
| \nocite{Gnedin:Krengel:1995} | |
| \nocite{Gnedin:Krengel:1996} | |
| \nocite{Gnedin:Krengel:1996} | |
| \nocite{Goldie:Rogers:1984} | |
| \nocite{Goldie:Resnick:1995} | |
| \nocite{Goldstein:Samuel-Cahn:2006} | |
| \nocite{Grun:2013} | |
| \nocite{Gusein-Sade:1967} | |
| \nocite{Haggstrom:1967} | |
| \nocite{Hamadene:2006} | |
| \nocite{Hamadene:Zhang:2010} | |
| \nocite{Hamadene:Hassani:2014a} | |
| \nocite{Hamadene:Hassani:2014b} | |
| \nocite{Hill:Kennedy:1992} | |
| \nocite{Hill:Kennedy:1994} | |
| \nocite{Hill:Kertz:1982} | |
| \nocite{Hill:Kertz:1992} | |
| \nocite{Hill:Krengel:1991} | |
| \nocite{Hill:Krengel:1992} | |
| \nocite{Hlynka:Sheahan:1988} | |
| \nocite{Hsiau:Yang:2000} | |
| \nocite{Hubert:Pyke:2000} | |
| \nocite{Immorlica:Kleinberg:Mahdian:2006} | |
| \nocite{Kadota:KuranoYasuda:2006} | |
| \nocite{Karpowicz:Szajowski:2007a} | |
| \nocite{Karpowicz:Szajowski:2007b} | |
| \nocite{Kawai:Tamaki:2003} | |
| \nocite{Kennedy:Kertz:1990} | |
| \nocite{Kennedy:Kertz:1991} | |
| \nocite{Kennedy:Kertz:1992a} | |
| \nocite{Kennedy:Kertz:1992b} | |
| \nocite{Kennedy:Kertz:1997} | |
| \nocite{Kifer:1971} | |
| \nocite{Kifer:2006} | |
| \nocite{Kifer:2013} | |
| \nocite{Krasnosielska:Ferenstein:2013} | |
| \nocite{Krieger:Pollak:SamuelCahn:2007} | |
| \nocite{Krieger:Pollak:SamuelCahn:2010} | |
| \nocite{Krieger:SamuelCahn:2009} | |
| \nocite{Krieger:SamuelCahn:2012} | |
| \nocite{Kubicki:Morayne:2005} | |
| \nocite{Kuchta:Morayne:2014} | |
| \nocite{Kuhne:Ruschendorf:2000a} | |
| \nocite{Kuhne:Ruschendorf:2000b} | |
| \nocite{Kurano:Nakagami:Yasuda:1980} | |
| \nocite{Lehtinen:1997} | |
| \nocite{Lehtinen:1993a} | |
| \nocite{Lehtinen:1993b} | |
| \nocite{Lindley:1961} | |
| \nocite{Loertscher:Muehlheusser:2011} | |
| \nocite{Lorenzen:1979} | |
| \nocite{Lorenzen:1981} | |
| \nocite{Ludkovski:2009} | |
| \nocite{Ludkovski:2011} | |
| \nocite{MacQueen:Miller:1960} | |
| \nocite{Mahdian:McAfee:Pennock:2008} | |
| \nocite{Maitra:Sudderth:1993} | |
| \nocite{Maitra:Sudderth:2000} | |
| \nocite{Majumdar:1985a} | |
| \nocite{Majumdar:1985b} | |
| \nocite{Mallows:Nair:Shepp:Vardi:1985} | |
| \nocite{Mazalov:Konovalchikova:2015} | |
| \nocite{Mazalov:Nosalskaya:Tokareva:2014} | |
| \nocite{Mashiah-Yaakovi:2014} | |
| \nocite{Matsui:Ano:2014} | |
| \nocite{Mazalov:Falko:2008} | |
| \nocite{Mazalov:Kochetov:1996} | |
| \nocite{Mazalov:Sakaguchi:2003} | |
| \nocite{McCardle:1985} | |
| \nocite{Morayne:1998} | |
| \nocite{Mori:1982a} | |
| \nocite{Mori:1982b} | |
| \nocite{Mori:1984} | |
| \nocite{Moriguti:1993a} | |
| \nocite{Moriguti:1993b} | |
| \nocite{Mucci:1973a} | |
| \nocite{Mucci:1973b} | |
| \nocite{Nakagami:1999} | |
| \nocite{Nakai:1985} | |
| \nocite{Nakai:1986a} | |
| \nocite{Nakai:1986b} | |
| \nocite{Nakai:1995} | |
| \nocite{Nakai:2006} | |
| \nocite{Nikolaev:1997} | |
| \nocite{Nikolaev:Sofronov:2007} | |
| \nocite{Neumann:Porosinski:Szajowski:1994} | |
| \nocite{Neumann:Ramsey:Szajowski:2002} | |
| \nocite{Nowak:Szajowski:1999} | |
| \nocite{Ohtsubo:1986} | |
| \nocite{Ohtsubo:1995} | |
| \nocite{Olsson:1974} | |
| \nocite{Peskir:1998} | |
| \nocite{Peskir:2008} | |
| \nocite{Petrucelli:1980} | |
| \nocite{Petrucelli:1981} | |
| \nocite{Petrucelli:1984} | |
| \nocite{Pfeifer:1989} | |
| \nocite{Pisinger:1997} | |
| \nocite{Porosinski:1987} | |
| \nocite{Porosinski:2002} | |
| \nocite{Porosinski:2003} | |
| \nocite{Porosinski:2004} | |
| \nocite{Porosinski:2005} | |
| \nocite{Porosinski:Szajowski:1996} | |
| \nocite{Preater:1994} | |
| \nocite{Preater:1998} | |
| \nocite{Preater:1999} | |
| \nocite{Presman:Sonin:1972} | |
| \nocite{Presman:Sonin:1975} | |
| \nocite{Presman:Sonin:2010} | |
| \nocite{Przykucki:Sulkowska:2010} | |
| \nocite{Quine:1980} | |
| \nocite{Quine:Robinson:1984} | |
| \nocite{Quine:Law:1996} | |
| \nocite{Radzik:Szajowski:1988} | |
| \nocite{Radzik:Szajowski:1990} | |
| \nocite{Ramsey:2008} | |
| \nocite{Ramsey:2011} | |
| \nocite{Ramsey:Cierpial:2009} | |
| \nocite{Ramsey:Szajowski:2001} | |
| \nocite{Ramsey:Szajowski:2004} | |
| \nocite{Ramsey:Szajowski:2006} | |
| \nocite{Ramsey:Szajowski:2008} | |
| \nocite{Rapoport:Seale:Winter:2002} | |
| \nocite{Rasmussen:Pliska:1976} | |
| \nocite{Rasmussen:1975} | |
| \nocite{Rasmussen:Pliska:1975} | |
| \nocite{Ravindran:Szajowski:1992} | |
| \nocite{Renault:Solan:Vieille:2013} | |
| \nocite{Righter:2011} | |
| \nocite{Rinott:SamuelCahn:1987} | |
| \nocite{Rinott:SamuelCahn:1992} | |
| \nocite{Robbins:1956} | |
| \nocite{Robbins:1970} | |
| \nocite{Robbins:Monro:1951} | |
| \nocite{Robbins:Siegmund:1970} | |
| \nocite{Robbins:Siegmund:1974a} | |
| \nocite{Robbins:Siegmund:1974b} | |
| \nocite{Robbins:Siegmund:1976} | |
| \nocite{Rocha:1993} | |
| \nocite{Rogerson:1987} | |
| \nocite{Rogerson:1988} | |
| \nocite{Rose:1982a} | |
| \nocite{Rose:1982b} | |
| \nocite{Rose:1982c} | |
| \nocite{Rose:1984} | |
| \nocite{Rosenberg:Solan:Vieille:2001} | |
| \nocite{Rosenberg:Solan:Vieille:2004} | |
| \nocite{Rubin:Samuels:1977} | |
| \nocite{Saario:1987} | |
| \nocite{Saario:1989} | |
| \nocite{Sackrowitz:SamuelCahn:1992} | |
| \nocite{Sakaguchi:1973} | |
| \nocite{Sakaguchi:1977} | |
| \nocite{Sakaguchi:1978} | |
| \nocite{Sakaguchi:1980} | |
| \nocite{Sakaguchi:1988a} | |
| \nocite{Sakaguchi:1988b} | |
| \nocite{Sakaguchi:1995a} | |
| \nocite{Sakaguchi:1995b} | |
| \nocite{Sakaguchi:1998} | |
| \nocite{Sakaguchi:2001a} | |
| \nocite{Sakaguchi:2001b} | |
| \nocite{Sakaguchi:2002a} | |
| \nocite{Sakaguchi:2002b} | |
| \nocite{Sakaguchi:2002c} | |
| \nocite{Sakaguchi:2003a} | |
| \nocite{Sakaguchi:2003b} | |
| \nocite{Sakaguchi:2004a} | |
| \nocite{Sakaguchi:2004b} | |
| \nocite{Sakaguchi:2004c} | |
| \nocite{Sakaguchi:2004d} | |
| \nocite{Sakaguchi:2004e} | |
| \nocite{Sakaguchi:2004f} | |
| \nocite{Sakaguchi:2004g} | |
| \nocite{Sakaguchi:2005a} | |
| \nocite{Sakaguchi:2005b} | |
| \nocite{Sakaguchi:2005c} | |
| \nocite{Sakaguchi:2006a} | |
| \nocite{Sakaguchi:2006b} | |
| \nocite{Sakaguchi:2006c} | |
| \nocite{Sakaguchi:2007a} | |
| \nocite{Sakaguchi:2007b} | |
| \nocite{Sakaguchi:2008} | |
| \nocite{Sakaguchi:Hamada:2000} | |
| \nocite{Sakaguchi:Hamada:2001} | |
| \nocite{Sakaguchi:Mazalov:2004} | |
| \nocite{Salminen:Teich:Wallenius:1998} | |
| \nocite{SamuelCahn:1974} | |
| \nocite{SamuelCahn:1984} | |
| \nocite{SamuelCahn:1992} | |
| \nocite{SamuelCahn:1995} | |
| \nocite{Samuels:1965} | |
| \nocite{Samuels:1969} | |
| \nocite{Samuels:1985} | |
| \nocite{Samuels:1992} | |
| \nocite{Samuels:2004} | |
| \nocite{Samuels:Steele:1981} | |
| \nocite{Schilling:2012} | |
| \nocite{Seale:Rapoport:1997} | |
| \nocite{Seale:Rapoport:2000} | |
| \nocite{Shapley:1953} | |
| \nocite{Shepp:1969} | |
| \nocite{Shepp:Shirayev:1996} | |
| \nocite{Shilony:1985} | |
| \nocite{Shmaya:Solan:2004} | |
| \nocite{Siegmund:1967} | |
| \nocite{Siegmund:1982} | |
| \nocite{Siegmund:1986} | |
| \nocite{Siegmund:1988} | |
| \nocite{Siegmund:2003} | |
| \nocite{Siegmund:Venkatraman:1995} | |
| \nocite{Siegmund:Yakir:2000a} | |
| \nocite{Siegmund:Yakir:2000b} | |
| \nocite{Simon:2007} | |
| \nocite{Smith:1975} | |
| \nocite{Smith:Deely:1975} | |
| \nocite{Solan:1999} | |
| \nocite{Solan:Vieille:2001} | |
| \nocite{Solan:Vieille:2002} | |
| \nocite{Solan:Vieille:2003} | |
| \nocite{Solan:Vieille:2004} | |
| \nocite{Sonin:1976} | |
| \nocite{Stadje:1985a} | |
| \nocite{Stadje:1985b} | |
| \nocite{Stadje:1987a} | |
| \nocite{Stadje:1987b} | |
| \nocite{Stadje:1997} | |
| \nocite{Stadje:2008} | |
| \nocite{Starr:1972} | |
| \nocite{Stein:Seale:Rapoport:2003} | |
| \nocite{Stewart:1978} | |
| \nocite{Stewart:1981} | |
| \nocite{Suchwalko:Szajowski:2002} | |
| \nocite{Suchwalko:Szajowski:2003} | |
| \nocite{Szajowski:1992} | |
| \nocite{Szajowski:1993} | |
| \nocite{Szajowski:1994} | |
| \nocite{Szajowski:1995} | |
| \nocite{Szajowski:Yasuda:1997} | |
| \nocite{Szajowski:2007} | |
| \nocite{Szajowski:2009} | |
| \nocite{Szajowski:2011} | |
| \nocite{Szajowski:Yasuda:1997} | |
| \nocite{Tamaki:1979a} | |
| \nocite{Tamaki:1979b} | |
| \nocite{Tamaki:1984} | |
| \nocite{Tamaki:1986} | |
| \nocite{Tamaki:1988} | |
| \nocite{Tamaki:1991} | |
| \nocite{Tamaki:2000} | |
| \nocite{Tamaki:2001} | |
| \nocite{Tamaki:2007} | |
| \nocite{Tamaki:2009} | |
| \nocite{Tamaki:2010} | |
| \nocite{Tamaki:2013} | |
| \nocite{Tamaki:Ohno:2000} | |
| \nocite{Tamaki:Pearce:Szajowski:2002} | |
| \nocite{Tamaki:Wang:2010} | |
| \nocite{Touzi:Vieille:2002} | |
| \nocite{Lawler:Vanderbei:1983} | |
| \nocite{Vanderbei:1980} | |
| \nocite{Sardelis:Valahas:1999} | |
| \nocite{Villareal:Karwan:1981a} | |
| \nocite{Villareal:Karwan:1981b} | |
| \nocite{Villareal:Karwan:1982} | |
| \nocite{Wang:Wang:Liu:2008} | |
| \nocite{Welch:1991} | |
| \nocite{Wilson:1991} | |
| \nocite{Yang:1982} | |
| \nocite{Yang:1974} | |
| \nocite{Yang:2009} | |
| \nocite{Yao:1997} | |
| \nocite{Yasuda:1984a} | |
| \nocite{Yasuda:1984b} | |
| \nocite{Yasuda:1985} | |
| \nocite{Yasuda:1988a} | |
| \nocite{Yasuda:1988b} | |
| \nocite{Yasuda:1995} | |
| \nocite{Yasuda:Nakagami:Kurano:1982} | |
| \nocite{Yeo:1998} | |
| \nocite{Yoshida:Yasuda:Nakagami:Kurano:2000} | |
| \nocite{Zuckerman:1986} | |
| \nocite{Zwick:Rapoport:1985} | |
| \btPrintCited | |
| \end{btSect} | |
| \end{btUnit} | |
| \end{document} |
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I have put together some references on the Secretary Problem. This is only a partial list. While I have most of these, there's about 5% of the articles listed here for which I do not have a PDF. And I have read only a fraction of the references compiled here, naturally.
I intend to highlight the survey articles, the articles on multi-player games, on the Dynkin game, in continuous time, with Bayesian learning. But this will require reading at least a couple of pages from each paper. And as this is a side project with no deadline, it's very likely I will not come back to this page for a while.