Find the optimal row or column strategy of the matrix game.
-Let $\mathrm { M }$ be the matrix game having payoff matrix $\left[ \begin{array} { r r r r } 1 & 1 & - 2 & 6 \ 0 & 4 & 5 & 3 \end{array} \right]$.
Find the optimal column strategy.
A) $\hat { y } = \left[ \begin{array} { c } \frac { 7 } { 8 } \ 0 \ \frac { 1 } { 8 } \ 0 \end{array} \right]$

B) $\hat { \mathrm { y } } = \left[ \begin{array} { c } \frac { 5 } { 8 } \ 0 \ \frac { 3 } { 8 } \ 0 \end{array} \right]$

C) $\hat { \mathrm { y } } = \left[ \begin{array} { c } \frac { 5 } { 8 } \ \frac { 3 } { 8 } \ 0 \ 0 \end{array} \right]$

D) $\hat { \mathrm { y } } = \left[ \begin{array} { c } \frac { 7 } { 8 } \ \frac { 1 } { 8 } \ 0 \ 0 \end{array} \right]$

Question

Find the optimal row or column strategy of the matrix game.
-Let $\mathrm { M }$ be the matrix game having payoff matrix $\left[ \begin{array} { r r r r } 1 & 1 & - 2 & 6 \ 0 & 4 & 5 & 3 \end{array} \right]$.
Find the optimal column strategy.
A) $\hat { y } = \left[ \begin{array} { c } \frac { 7 } { 8 } \ 0 \ \frac { 1 } { 8 } \ 0 \end{array} \right]$

B) $\hat { \mathrm { y } } = \left[ \begin{array} { c } \frac { 5 } { 8 } \ 0 \ \frac { 3 } { 8 } \ 0 \end{array} \right]$

C) $\hat { \mathrm { y } } = \left[ \begin{array} { c } \frac { 5 } { 8 } \ \frac { 3 } { 8 } \ 0 \ 0 \end{array} \right]$

D) $\hat { \mathrm { y } } = \left[ \begin{array} { c } \frac { 7 } { 8 } \ \frac { 1 } { 8 } \ 0 \ 0 \end{array} \right]$

Quizplus · Accepted Answer

The optimal column strategy can be found by solving the linear programming problem that maximizes the minimum gain for the column player. In this case, the optimal strategy is $\hat { y } = \left[ \frac { 7 } { 8 }, 0, \frac { 1 } { 8 }, 0 \right]$ because it ensures the highest minimum payoff for the column player given the row player's strategies.

Find the Optimal Row or Column Strategy of the Matrix M\mathrm { M }M

Find the Optimal Row or Column Strategy of the Matrix $\mathrm { M }$