*z*= f(rock,paper,scissors) = f (x1,x2,x3) equal to some payoff value

*v,*subject to the following game conditions:

to solve in Matlab, we must rearrange the constraints to include

*v*as a variable (right). The game matrix is:

A = [0 -1 1 1; 1 0 -1 1; -1 1 0 1];

b = [0 0 0];

Aeq = [1 1 1 0];

beq = 1;

lb = [0 0 0 -inf]; % here the lower bound of v has not to necessarily zero, but in a general game could be minus infinity.

% Objective function

f = [0 0 0 -1];

% Solve the LP

z = linprog(f,A,b,Aeq,beq,lb);

% Payoff

v = z(4)

% Probability of the variables

x = z(1:3)

v =

0

x =

0.3333

0.3333

0.3333

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