📚 Learning Guide
Nash Equilibrium in Game Theory
hard

In a two-player game, if both players are using a mixed strategy to maximize their payoffs and reach a Nash Equilibrium, which of the following statements is true?

Master this concept with our detailed explanation and step-by-step learning approach

Learning Path
Learning Path

Question & Answer
1
Understand Question
2
Review Options
3
Learn Explanation
4
Explore Topic

Choose the Best Answer

A

Both players are playing pure strategies.

B

At least one player is indifferent between their strategies.

C

The players can improve their payoffs by unilaterally changing their strategies.

D

The game has multiple Nash Equilibria with only one being stable.

Understanding the Answer

Let's break down why this is correct

Answer

In a two-player game, when both players use a mixed strategy to reach a Nash Equilibrium, it means that each player is choosing their actions based on probabilities rather than sticking to one specific choice. This situation occurs when neither player can improve their payoff by changing their strategy while the other player's strategy remains the same. For example, imagine a game where Player A can choose between two actions, A1 and A2, and Player B can choose between B1 and B2. If Player A mixes their choices and Player B does the same, they may both end up with a stable outcome where neither has an incentive to switch strategies. Therefore, at Nash Equilibrium, both players are making the best decisions they can, given what the other is doing.

Detailed Explanation

In a Nash Equilibrium, at least one player feels that changing their strategy won't help them. Other options are incorrect because Some might think both players are using fixed strategies; It's a common mistake to think players can always do better by changing strategies.

Key Concepts

Nash Equilibrium
mixed strategy
pure strategy
Topic

Nash Equilibrium in Game Theory

Difficulty

hard level question

Cognitive Level

understand

Ready to Master More Topics?

Join thousands of students using Seekh's interactive learning platform to excel in their studies with personalized practice and detailed explanations.