Question

Microeconomics

Posted 2 months ago

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- 4. Use the matrix below to answer the following questions:
- A) What is Keisha's dominant strategy? Explain
- B) What is Larry's dominant strategy? Explain
C) What is the Nash equilibrium in this situation? Explain.
- D) Is the Nash equilibrium Pareto optimal? Why/why not?
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Answer from Sia

Posted 2 months ago

Solution

a

Keisha's Dominant Strategy: A dominant strategy is one that results in a higher payoff for a player, regardless of the opponent's action. For Keisha, if Larry confesses, Keisha gets 10 years if she confesses and 30 years if she keeps quiet. If Larry keeps quiet, Keisha goes free if she confesses and gets 1 year if she keeps quiet. Therefore, Keisha's dominant strategy is to confess

b

Larry's Dominant Strategy: Similarly, for Larry, if Keisha confesses, Larry gets 10 years if he confesses and 30 years if he keeps quiet. If Keisha keeps quiet, Larry goes free if he confesses and gets 1 year if he keeps quiet. Therefore, Larry's dominant strategy is to confess

c

Nash Equilibrium: A Nash equilibrium occurs when each player's strategy is optimal, given the strategy of the other player. Since both Keisha and Larry have dominant strategies to confess, the Nash equilibrium is (Confess, Confess), where both receive 10 years in jail

d

Pareto Optimality: A situation is Pareto optimal if no player can be made better off without making the other player worse off. In this case, the Nash equilibrium (Confess, Confess) is not Pareto optimal because both players would be better off if they both kept quiet, receiving only 1 year each

Answer

- Keisha's dominant strategy: Confess
- Larry's dominant strategy: Confess
- Nash equilibrium: (Confess, Confess)
- Pareto optimality: No, it is not Pareto optimal

Key Concept

Dominant Strategy

Explanation

A dominant strategy is the best action for a player, regardless of what the opponent does. In this scenario, both Keisha and Larry have dominant strategies to confess.

Key Concept

Nash Equilibrium

Explanation

A Nash equilibrium is a set of strategies where no player can benefit by unilaterally changing their strategy. Here, both confessing is the Nash equilibrium.

Key Concept

Pareto Optimality

Explanation

A situation is Pareto optimal if no player can be made better off without making the other player worse off. The Nash equilibrium in this case is not Pareto optimal because both players could be better off by keeping quiet.

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