91Ó°ÊÓ

Determine the maximin and minimax strategies for each two-person, zero-sum matrix game. $$ \left[\begin{array}{ll} 2 & 3 \\ 4 & 1 \end{array}\right] $$

Determine which of the matrices are regular. $$ \left[\begin{array}{ll} \frac{2}{5} & \frac{3}{4} \\ \frac{3}{5} & \frac{1}{4} \end{array}\right] $$

Determine which of the matrices are stochastic. \(\left[\begin{array}{ll}.4 & .7 \\ .6 & .3\end{array}\right]\)

Determine whether the matrix is an absorbing stochastic matrix. \(\left[\begin{array}{ll}\frac{2}{5} & 0 \\ \frac{3}{5} & 1\end{array}\right]\)

Find the expected payoff \(E\) of each game whose payoff matrix and strategies \(P\) and \(Q\) (for the row and column players, respectively) are given. \(\left[\begin{array}{rr}3 & 1 \\ -4 & 2\end{array}\right], P=\left[\begin{array}{ll}\frac{1}{2} & \frac{1}{2}\end{array}\right], Q=\left[\begin{array}{l}\frac{3}{5} \\ \frac{2}{5}\end{array}\right]\)

Determine the maximin and minimax strategies for each two-person, zero-sum matrix game. $$ \left[\begin{array}{rr} -1 & 3 \\ 2 & 5 \end{array}\right] $$

Determine which of the matrices are stochastic. \(\left[\begin{array}{rr}.8 & .2 \\ .3 & .7\end{array}\right]\)

Determine whether the matrix is an absorbing stochastic matrix. \(\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\)

Determine which of the matrices are regular. $$ \left[\begin{array}{ll} 0 & .3 \\ 1 & .7 \end{array}\right] $$

Find the expected payoff \(E\) of each game whose payoff matrix and strategies \(P\) and \(Q\) (for the row and column players, respectively) are given. \(\left[\begin{array}{rr}-1 & 4 \\ 3 & -2\end{array}\right], P=\left[\begin{array}{ll}.8 & .2\end{array}\right], Q=\left[\begin{array}{l}.6 \\\ .4\end{array}\right]\)