Solve the Problem $$\text { Find the optimal strategy for player } R \text {. }$$

question 48

Multiple Choice

Solve the problem.
-Player R has two cards: a red 2 and a black 8. Player C has three cards: a red 3, a black 5, and a black 10. They each show one of their cards. If the cards are the same color, C receives the larger of
The two numbers. If the cards are of different colors, R receives the sum of the two numbers. The
Payoff matrix is :
$$\text { Find the optimal strategy for player } R \text {. }$$

• A) \(\hat{x}=\left[\begin{array}{l} \frac{19}{29} \\ \frac{10}{29} \end{array}\right]\)
• B) \(\hat{x}=\left[\begin{array}{l} \frac{2}{3} \\ \frac{1}{3} \end{array}\right]\)
• C) \(\hat{x}=\left[\begin{array}{l} 1 \\ 0 \end{array}\right]\)
• D) \(\hat{x}=\left[\begin{array}{l} \frac{10}{29} \\ \frac{19}{29} \end{array}\right]\)

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Definitions:

Empathy

The ability to understand and share the feelings of another person.

Internal Reality

An individual's subjective perception of their thoughts, feelings, and experiences.

Defense Mechanisms

Psychological strategies unconsciously employed to protect oneself from anxiety and the unacceptable aspects of reality.

Differentiation

The process of identifying and defining one's own thoughts, feelings, and actions as distinct from those of others, often used in the context of family systems theory.