Find the Optimal Row or Column Strategy of the Matrix $M$

question 9

Multiple Choice

Find the optimal row or column strategy of the matrix game.
-Let $M$ be the matrix game having payoff matrix $\left[ \begin{array} { r r r r r } 1 & 1 & 3 & - 1 & 4 \\ 1 & - 2 & - 1 & 1 & - 2 \\ 2 & - 1 & 0 & 3 & - 2 \end{array} \right]$ .
Find the optimal row strategy.

• A) \(\hat { x } = \left[ \begin{array} { c } \frac { 1 } { 3 } \\ 0 \\ \frac { 2 } { 3 } \end{array} \right]\)
• B) \(\hat { x } = \left[ \begin{array} { c } \frac { 2 } { 3 } \\ 0 \\ \frac { 1 } { 3 } \end{array} \right]\)
• C) \(\hat { x } = \left[ \begin{array} { c } \frac { 1 } { 2 } \\ \frac { 1 } { 6 } \\ \frac { 1 } { 3 } \end{array} \right]\)
• D) \(\hat { x } = \left[ \begin{array} { c } \frac { 1 } { 2 } \\ 0 \\ \frac { 1 } { 2 } \end{array} \right]\)

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Definitions:

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