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In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player iis described as follows: There are two "statuses" that player i might be in during any period: "normal" and "revenge"; . In a normal status player i cooperates; In a revenge status player i defects; From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period; . From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player's action in this period.

In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player iis described as follows: There are two "statuses" that player i might be in during any period: "normal" and "revenge"; . In a normal status player i cooperates; In a revenge status player i defects; From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period; . From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player's action in this period.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter13: best-practice Tactics: Game Theory
Section: Chapter Questions
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8. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player i is described as follows: There are two "statuses" that player i might be in during any period: "normal" and "revenge"; . In a normal status player i cooperates; . In a revenge status player i defects; From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period; From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player's action in this period. Consider an infinitely repeated game so that with probability p that the game continues to the next period and with probability (1-p) it ends. Defect (D) Cooperate (C) 4,4 0,5 Cooperate (C) Defect (D) 5,0 1,1 What is the payoff for player 2 from always cooperating when player 1 uses this tit for tat strategy and begins in a normal status? How about always defecting when 1 begins in a normal status? O a) 4 + 4p + 4p² +. 4p³ + ...; b) 4 + 4p + 4p² + 4p³ +...; O c) 5+ 4p + 4p² + 4p³ + ...; O d) 5+ 4p + 4p² + 4p³ + ...; 5+p+p²+p³ +... 5+p+5p²+p³ +... 4 + 4p + 4p² + 4p³ + ... 5+p+p² +p³ +...
Transcribed Image Text:8. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player i is described as follows: There are two "statuses" that player i might be in during any period: "normal" and "revenge"; . In a normal status player i cooperates; . In a revenge status player i defects; From a normal status, player i switches to the revenge status in the next period only if the other player defects in this period; From a revenge status player i automatically switches back to the normal status in the next period regardless of the other player's action in this period. Consider an infinitely repeated game so that with probability p that the game continues to the next period and with probability (1-p) it ends. Defect (D) Cooperate (C) 4,4 0,5 Cooperate (C) Defect (D) 5,0 1,1 What is the payoff for player 2 from always cooperating when player 1 uses this tit for tat strategy and begins in a normal status? How about always defecting when 1 begins in a normal status? O a) 4 + 4p + 4p² +. 4p³ + ...; b) 4 + 4p + 4p² + 4p³ +...; O c) 5+ 4p + 4p² + 4p³ + ...; O d) 5+ 4p + 4p² + 4p³ + ...; 5+p+p²+p³ +... 5+p+5p²+p³ +... 4 + 4p + 4p² + 4p³ + ... 5+p+p² +p³ +...
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