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

question 12

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) \(\hat { x } = \left[ \begin{array} { l } 0 \\ 1 \end{array} \right] , \hat { y } = \left[ \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right]\)

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Definitions:

Gender-typing

The process of adopting roles and behaviors considered culturally appropriate for one's gender.

Gender Differ

The variations in characteristics, roles, behaviors, and expectations based on the social construct of gender.

Physically Aggressive

Exhibiting behaviors that involve physical harm or the intention to harm others.

Empathetic

Having the ability to understand and share the feelings of another.