In an extensive form game, if Player A chooses to cooperate while Player B has the option to defect, what will Player B's optimal strategy be using backward induction?

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Cooperate

Defect

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Ignore Player A's move

Understanding the Answer

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Answer

When we work backwards through the game tree, we first look at the point where Player B must decide. If B defects, B gets a higher payoff than if B cooperates, no matter what A did earlier. Because B’s choice is made after seeing A’s cooperate, B compares the two outcomes and picks the higher one. Thus, backward induction tells us that B’s optimal strategy is to defect. For example, if cooperating gives B 1 and defecting gives B 3, B will choose defect.

Detailed Explanation

Backward induction means we look at the last move first. Other options are incorrect because Some think cooperation is best because it is kind; Randomly choosing does not maximize payoff.

Key Concepts

extensive form games

Topic

Game Theory and Backward Induction

Difficulty

easy level question

Cognitive Level

understand

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Question 4

In a sequential game, how does backward induction impact a player's strategy selection?

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Question 6

In a competitive game scenario where two players must decide their next move while anticipating each other's responses, which strategy best utilizes backward induction for optimal decision-making?

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Question 7

Arrange the steps a player should take in a game theory scenario using backward induction to maximize their strategy: A) Analyze potential outcomes and payoffs, B) Decide on the current move based on the analysis, C) Observe the opponent's previous moves, D) Make an informed strategy choice based on the observed responses.

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Question 8

In a two-player game scenario, which of the following strategies can effectively leverage backward induction to anticipate an opponent's moves? Select all that apply.

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