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) \(\hat { x } = \left[ \begin{array} { c } \frac { 1 } { 2 } \\ 0 \\ \frac { 1 } { 2 } \end{array} \right]\)

Understand concepts of normal and inferior goods.

Grasp the factors affecting demand elasticity.

Understand the relationship between price changes and demand elasticity.

Grasp how production levels correlate with current and desired margins.

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Definitions:

Agency Relationships

A legal relationship where one party, the agent, is authorized to act on behalf of another party, the principal, in business transactions.

Gratuitous Agent

An agent who acts on behalf of another without any compensation for their services.

Duty Of Loyalty

An obligation of fiduciaries to act in the best interest of the beneficiaries or the entities they serve, avoiding conflicts of interest.

Sales Agent

An individual or entity authorized to sell and market products or services on behalf of another party, known as the principal.