Solve the Problem $$\left[ \begin{array} { l l l } a _ { 11 } & a _ { 12 } & a _ { 13 } \\a _ { 21 } & a _ { 22 } & a _ { 23 }\end{array} \right]$$

Multiple Choice

Solve the problem.
-A matrix game has payoff matrix
$$\left[ \begin{array} { l l l } a _ { 11 } & a _ { 12 } & a _ { 13 } \\a _ { 21 } & a _ { 22 } & a _ { 23 }\end{array} \right]$$
in which entry a 21 is a saddle point. What are the optimal strategies for player $\mathrm { R }$ and player C?

A) $\hat { x } = \left[ \begin{array} { c } \frac { 1 } { 2 } \\ \frac { 1 } { 2 } \end{array} \right] , \hat { y } = \left[ \begin{array} { c } \frac { 1 } { 3 } \\ \frac { 1 } { 3 } \\ \frac { 1 } { 3 } \end{array} \right]$
B) $\hat { x } = \left[ \begin{array} { l } 0 \\ 1 \end{array} \right] , \hat { y } = \left[ \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right]$
C) $\hat { \mathrm { x } } = \left[ \begin{array} { l } 1 \\ 0 \end{array} \right] , \hat { \mathrm { y } } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$
D) $\hat { x } = \left[ \begin{array} { l } 0 \\ 1 \end{array} \right] , \hat { y } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]$