ProblemTFT

# ProblemTFT - rounds B Suppose that Player 2 is using a...

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Homework Question Two players play a prisoner’s dilemma game repeatedly. There are two possible actions in each round of play, C (cooperate) and D (defect). In any round, if both players cooperate, each gets a payoﬀ of \$5 for that round. If both defect, each gets a payoﬀ of \$1 for that round. If one player cooperates and the other defects, the one who defects gets a payoﬀ of \$6 and the one who cooperates gets a payoﬀ of \$0. After each round of play, two fair coins are tossed. If both come up heads, the game ends. If the outcome is anything else, both are told what the other die on the previous round and another round is played. Total payoﬀ to a player is the sum of the payoﬀs he or she earns in each round that is played. A) If both players cooperate on every play until the game ends, what is the expected total payoﬀ to each player? (Hints: The answer is found by summing a geometric series. What is the probability that the game lasts for at least K
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Unformatted text preview: rounds?) B) Suppose that Player 2 is using a “grim trigger” strategy, where he will cooperate so long as Player 1 cooperates, but if Player 1 ever defects, Player 2 will defect forever. What is the highest expected total payoﬀ that Player 1 could get if he plays defect on the ﬁrst move? Is there a Nash equilibrium in which both players play the grim trigger strategy? Explain your answer. C) Suppose that Player 2 plays a “tit-for-tat” strategy in which he cooperates on the ﬁrst move and in all later periods he uses the same action that Player 1 took on the preceding move. What would be the expected payoﬀ to Player 1 if he played Defect on his ﬁrst move and then played cooperate in all future moves? Is there a Nash equilibrium in which both players play the “tit-for-tat” strategy? Explain your answer. 1...
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## This note was uploaded on 12/25/2011 for the course ECON 171 taught by Professor Charness,g during the Fall '08 term at UCSB.

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