A saddle point is supposed to be a saddle-point in the multi-variable calculus sense: it is...

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A saddle point is supposed to be a saddle-point in the multi-variable calculus sense: it is the max for PI's variables and the min for P2's variables. So we should be able to find it by looking for critical points! Consider the game with matrix Y 1-4 devi 4 2 1 6 X 1-x (a) Write down the expected payoff p(x, y) to P1 if P1 plays (r, 1-r) and P2 plays (y, 1-y). (b) At a saddle point, partial derivatives are supposed to be 0. Calculate pz(x, y), and p,(x, y), and solve the equations pr(x, y) = py(x, y) = 0 to find the saddle point in the calculus sense. What does this predict the optimal strategies should be? (c) Now solve the game using indifference equations. Make sure you get the same answer. In fact, you should even get the same equations.... (d) Now start going down this path with the matrix. 1-4 4 *(?). 51 1-4 1-5 1-5 1-1 A saddle point is supposed to be a saddle-point in the multi-variable calculus sense: it is the max for PI's variables and the min for P2's variables. So we should be able to find it by looking for critical points! Consider the game with matrix Y 1-4 devi 4 2 1 6 X 1-x (a) Write down the expected payoff p(x, y) to P1 if P1 plays (r, 1-r) and P2 plays (y, 1-y). (b) At a saddle point, partial derivatives are supposed to be 0. Calculate pz(x, y), and p,(x, y), and solve the equations pr(x, y) = py(x, y) = 0 to find the saddle point in the calculus sense. What does this predict the optimal strategies should be? (c) Now solve the game using indifference equations. Make sure you get the same answer. In fact, you should even get the same equations.... (d) Now start going down this path with the matrix. 1-4 4 *(?). 51 1-4 1-5 1-5 1-1

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2 2 a The expected payoff to P1 if P1 plays r1r and P2 plays y1y is given by the dot product of the ... View the full answer