MathProg: calculate mixed strategies Nash equilibrium (2 players, 0-sum game)

0s.dat

data;

set P1S := a b c;
set P2S := 1 2 3 4;

param Payoff
    :  1  2  3  4 :=
    a  -5 3  1  8
    b  5  5  4  6
    c  -4 6  0  5;

end;

0sp1.mod

set P1S;
set P2S;

param Payoff{P1S, P2S};

var y{P1S} >= 0;

minimize GameValue: sum{i in P1S} y[i];

s.t. Condition2{j in P2S}:
    sum{i in P1S} Payoff[i,j] * y[i] >= 1;

solve;

printf "Value: %s\n", GameValue;

printf "Player 1 strategies:\n";

for{i in P1S}
    printf "Found %s, actual %s\n", y[i], y[i]/GameValue; 

end;

0sp2.mod

set P1S;
set P2S;

param Payoff{P1S, P2S};

var x{P2S} >= 0;

maximize GameValue: sum{j in P2S} x[j];

s.t. Condition1{i in P1S}:
    sum{j in P2S} Payoff[i,j] * x[j] <= 1;

solve;

printf "Value: %s\n", GameValue;

printf "Player 2 strategies:\n";

for{j in P2S}
    printf "Found %s, actual %s\n", x[j], x[j]/GameValue;

end;