📚 Learning Guide
Nash Equilibrium in Game Theory
hard

In a coordination game where two players choose between two strategies, if both players have a dominant strategy that leads to different outcomes, which of the following statements best describes the situation regarding Nash Equilibrium?

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Choose the Best Answer

A

There will be multiple Nash Equilibria in this game.

B

There will be no Nash Equilibrium as both players cannot agree on their strategies.

C

There will be a unique Nash Equilibrium where both players choose their dominant strategies.

D

The players will achieve the best outcome by randomizing their strategies.

Understanding the Answer

Let's break down why this is correct

Answer

In a coordination game, a Nash Equilibrium occurs when both players choose strategies that they have no incentive to change, given the choice of the other player. If both players have a dominant strategy that leads to different outcomes, it means each player has a preferred choice that they will stick to, even if it doesn't match the other player's preference. For example, if Player A's dominant strategy is to choose "X" and Player B's dominant strategy is to choose "Y," they will each choose their strategies, resulting in a situation where neither has a reason to switch to the other's choice. However, this can create a mismatch and lead to an outcome that is not optimal for both. Therefore, in this case, there is no Nash Equilibrium since the players' choices do not align, leaving them potentially worse off than if they could coordinate their strategies.

Detailed Explanation

In this case, neither player can agree on a strategy. Other options are incorrect because Some might think there can be many stable choices; It's a common mistake to think that dominant strategies always lead to one stable choice.

Key Concepts

strategic interaction
dominant strategy
coordination games.
Topic

Nash Equilibrium in Game Theory

Difficulty

hard level question

Cognitive Level

understand

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