How do I find Nash Equilibria if I have Payoff functions instead of Payoff Matrix in MATLAB?
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I want to find Nash Equilibrium. Two objective functions are
J1= - P1 = - (6885376000000*x1*(5000*x2 + 261)^2)/(1050003000*x1 + 1050003000*x2 + 13555000000*x1*x2 + 72685107)^2 and
J2= - P2 = - (6885376000000*x2*(5000*x1 + 261)^2)/(1050003000*x1 + 1050003000*x2 + 13555000000*x1*x2 + 72685107)^2.
Here x1 and x2 are the two control variables of Two player A and B respectively. Now I want to find Nash Equilibrium in the matlab. (Actually I read/studied Prisoner's dilemma etc where Payoff is in matrix but here it is function. That's why I don't have any idea)
x1_optimal = L(x2)= arg min J1(x1,x2)
x1
x2_optimal = L(x1)= arg min J2(x1,x2)
x2
Also I want to plot figure x1 and x2 where one is in x axis and other is in y axis and intersection shows the Nash Equilibrium point. How shoul I code it in MATLAB? Please help me. Thanks.
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