3.I.5H3 . \mathrm{I} . 5 \mathrm{H} \quad

Optimization | Part IB, 2002

Consider a two-person zero-sum game with a payoff matrix

(3b52)\left(\begin{array}{ll} 3 & b \\ 5 & 2 \end{array}\right)

where 0<b<0<b<\infty. Here, the (i,j)(i, j) entry of the matrix indicates the payoff to player one if he chooses move ii and player two move jj. Suppose player one chooses moves 1 and 2 with probabilities pp and 1p,0p11-p, 0 \leq p \leq 1. Write down the maximization problem for the optimal strategy and solve it for each value of bb.

Typos? Please submit corrections to this page on GitHub.