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Game Theory and Backward Induction
hard

In a game involving two players, Player A has a dominant strategy to choose Action X, while Player B has a mixed strategy involving a probability of playing Action Y. If the payoff matrix indicates that Action X guarantees a payoff of 10 for Player A regardless of Player B's choice, what can be concluded about Player B's optimal strategy?

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Learning Path
Learning Path

Question & Answer
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Choose AnswerChoose the Best Answer

A

Player B should always play Action Y

B

Player B's best response can vary based on the chosen probability

C

Player B should never play Action Y

D

Player B will always achieve a higher payoff by choosing Action Y

Understanding the Answer

Let's break down why this is correct

Because Player A always gets 10 no matter what, Player B's payoff depends only on B's own choices. Other options are incorrect because Thinking that B must always play Y ignores that B's payoff can be higher with other actions; Believing B should never play Y assumes Y is bad, but Y might give B a good payoff when A plays X.

Key Concepts

dominant strategy
mixed strategies
game payoff
Topic

Game Theory and Backward Induction

Difficulty

hard level question

Cognitive Level

understand

Deep Dive: Game Theory and Backward Induction

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Definition
Definition

Game theory is a mathematical framework used to analyze strategic interactions among rational decision-makers. Backward induction is a method used to solve sequential move games, where players make decisions based on the observed actions of others, as illustrated by the game tree format. This concept is significant in business as it helps understand competitive behavior and decision-making processes in various strategic situations.

Topic Definition

Game theory is a mathematical framework used to analyze strategic interactions among rational decision-makers. Backward induction is a method used to solve sequential move games, where players make decisions based on the observed actions of others, as illustrated by the game tree format. This concept is significant in business as it helps understand competitive behavior and decision-making processes in various strategic situations.

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