📚 Learning Guide
Nash Equilibrium in Game Theory
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In a game involving two players, Player A has a dominant strategy of choosing option X, while Player B's payoff matrix indicates that choosing option Y is best regardless of Player A's choice. What can be concluded about the Nash Equilibrium in this scenario?

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Choose the Best Answer

A

The Nash Equilibrium is at Player A choosing X and Player B choosing Y.

B

The Nash Equilibrium does not exist in this game.

C

Both players will deviate from their strategies leading to a higher payoff.

D

The Nash Equilibrium is at Player A choosing Y and Player B choosing X.

Understanding the Answer

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Answer

In this game, we see that Player A has a dominant strategy of choosing option X, meaning that X is the best choice for A no matter what Player B does. On the other hand, Player B's payoff matrix shows that option Y is the best choice for them, regardless of whether Player A chooses X or not. Since both players are making the best choices for themselves given the other's decision, we can conclude that the combination of Player A choosing X and Player B choosing Y is a Nash Equilibrium. This means that neither player has an incentive to change their strategy because they are already maximizing their payoffs. For example, if Player A sticks with X and Player B with Y, they both achieve their best possible outcomes based on the other’s choice.

Detailed Explanation

In this game, Player A will always choose X, and Player B will always choose Y. Other options are incorrect because Some might think that if players have strategies, there can't be a stable outcome; It's a common mistake to believe players will always try to change their strategies for better results.

Key Concepts

dominant strategy
payoff matrix
Topic

Nash Equilibrium in Game Theory

Difficulty

medium level question

Cognitive Level

understand

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