91Ó°ÊÓ

Determine the maximin and minimax strategies for each two-person, zero-sum matrix game. $$ \left[\begin{array}{rrr} 1 & 3 & 2 \\ 0 & -1 & 4 \end{array}\right] $$

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

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. \(\left[\begin{array}{rr}-4 & 3 \\ 2 & 1\end{array}\right], P=\left[\begin{array}{ll}\frac{1}{3} & \frac{2}{3}\end{array}\right], Q=\left[\begin{array}{l}\frac{3}{4} \\ \frac{1}{4}\end{array}\right]\)

Determine which of the matrices are stochastic. \(\left[\begin{array}{ll}\frac{1}{4} & \frac{1}{3} \\ \frac{3}{4} & \frac{7}{8}\end{array}\right]\)

Determine which of the matrices are regular. $$ \left[\begin{array}{ll} 1 & .8 \\ 0 & .2 \end{array}\right] $$

Determine the maximin and minimax strategies for each two-person, zero-sum matrix game. $$ \left[\begin{array}{lll} 1 & 4 & -2 \\ 4 & 6 & -3 \end{array}\right] $$

Determine which of the matrices are stochastic. \(\left[\begin{array}{lll}\frac{1}{3} & 0 & \frac{1}{2} \\ \frac{1}{2} & 1 & 0 \\\ \frac{1}{4} & 0 & \frac{1}{2}\end{array}\right]\)

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. \(\left[\begin{array}{rr}1 & 2 \\ -3 & 1\end{array}\right], P=\left[\begin{array}{ll}\frac{3}{5} & \frac{2}{5}\end{array}\right], Q=\left[\begin{array}{l}\frac{1}{3} \\ \frac{2}{3}\end{array}\right]\)

Determine which of the matrices are regular. $$ \left[\begin{array}{ll} \frac{1}{3} & 0 \\ \frac{2}{3} & 1 \end{array}\right] $$

Determine whether the matrix is an absorbing stochastic matrix. \(\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & .7 & .2 \\ 0 & .3 & .8\end{array}\right]\)