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

---

Definitions:

Fixed Resource

A resource whose quantity cannot easily be changed in the short term, such as land, buildings, or equipment.

Accounting Profit

The difference between total revenue and total explicit costs, not accounting for implicit costs, according to traditional accounting methods.

Entrepreneur's Potential Earnings

Entrepreneur's potential earnings are the anticipated income an entrepreneur expects to generate from their business ventures, considering the risks and opportunities involved.

Annual Lease

is a contract specifying the terms under which one party agrees to rent property from another party for a period of one year.