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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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9. In an infinitely repeated Prisoner's Dilemma, a version of what is known as a "tit for tat" strategy of a player 2 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. Cooperate (C) Defect (D) Cooperate (C) 4,4 5,0 Defect (D) 0,5 1,1 What is the threshold p* such that when p≥ p* always cooperating by player 2 is a best response to player 1 playing tit for tat and starting in a normal status, but when p < p*…
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