Question #55320

Consider the following game. The game has two players, and each player is asked a question. The players can answer a question honestly or they can lie. If both answer honestly, each receives a payoff of $100. If one player answers honestly and the other player lies, the liar gains at the expense of the honest player. In that event, the liar receives a payoff of $500 and the honest player gets nothing. If both lie, then each receives a payoff of $50.
(a) Construct the payoff matrix.
(b) What is the non-cooperative (Nash) equilibrium for this game? Explain how you have arrived at this answer.
(c) What is the optimum outcome? Is it likely to be reached? Explain.
(d) What is a “tit-for-tat” strategy? Why is it a rational strategy for the infinitely repeated prisoners’ dilemma?

Expert's answer

(a) The payoff matrix:

Player B

Lie Honest

Lie 50/50 500/0

Player A Honest 0/500 100/100

(b) The non-cooperative (Nash) equilibrium for this game is when both lie (50/50), because both players will afraid to be honest to receive the money.

(c) The optimum outcome is not likely to be reached, because both players think the other to lie.

(d) The tit for tat game theory is an expression in the mathematical area of game theory, relevant to a problem called the iterated prisoner's dilemma. It is a rational strategy for the infinitely repeated prisoners’ dilemma.

Player B

Lie Honest

Lie 50/50 500/0

Player A Honest 0/500 100/100

(b) The non-cooperative (Nash) equilibrium for this game is when both lie (50/50), because both players will afraid to be honest to receive the money.

(c) The optimum outcome is not likely to be reached, because both players think the other to lie.

(d) The tit for tat game theory is an expression in the mathematical area of game theory, relevant to a problem called the iterated prisoner's dilemma. It is a rational strategy for the infinitely repeated prisoners’ dilemma.

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