Chapter 11.2, Problem 2E

Suppose a game has payoff matrix $\left[\begin{array}{ccc}0& -4& 1\\ 3& 2& -4\\ 1& -1& 0\end{array}\right]$. Find the expected value of the game for the following strategies for players A and B.

(a) $A=\left[\begin{array}{ccc}0.1& 0.4& 0.5\end{array}\right];B=\left[\begin{array}{c}0.2\\ 0.4\\ 0.4\end{array}\right]$

(b) $A=\left[\begin{array}{ccc}0.3& 0.4& 0.3\end{array}\right];B=\left[\begin{array}{c}0.8\\ 0.1\\ 0.1\end{array}\right]$