asd

influence_game.py

"""
    Consider an n-player game, where each player x has influence i_x.
    At each round, each pair of players x, y flip a fair coin, and the
    winner gains i_x * i_y influence from the other player.
    
    The formula ensures that stakes are proportional to influence:
    Player x puts a greater stake towards a player y than player z
    when i_y > i_z.
"""

import numpy as np
from random import random

def play(influence):
    for i in range(n):
        for j in range(i):
            stake = influence[i] * influence[j]
            x = random() - 0.5
            s = x / np.abs(x)
            influence[i] += s * stake
            influence[j] -= s * stake

"""
    Initialize n players with equal influence:
"""
n = 100
influence = np.array([1 / n for _ in range(n)])

for _ in range(1000):
    play(influence)

"""
    After some time, almost all influence is concentrated to a single player.
"""
print(influence)