Infinitely Repeated Prisoner's DilemmaCooperate Defect(а, а)(b, с)(c, b)(d, d)СоорerateDefectHere, a = 16,6 = 1,c=18, d = 7. Assume that both of the players are playing the grim trigger strategy. Also assume that the discounting factor forboth player 1 and 2 is d.1. What is the payoff/utility of player 1 if both players decide to defect all the time? Assume 8 = 0.59.Write at least 3 digits after the decimal place.2. What is the payoff/utility of player 1 if both players decide to cooperate all the time? Assume d = 0.65.Write at least 3 digits after the decimal place.3. Find the minimum value of 5 for which player 1 will have no incentive to defect on the first stage, assuming player 1 and 2 both are playing grimtrigger strategy.Write at least 3 digits after the decimal place.

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Infinitely Repeated Prisoner's Dilemma

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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Question

Infinitely Repeated Prisoner's Dilemma
Cooperate Defect
(а, а)
(b, с)
(c, b)
(d, d)
Соорerate
Defect
Here, a = 16,6 = 1,c=18, d = 7. Assume that both of the players are playing the grim trigger strategy. Also assume that the discounting factor for
both player 1 and 2 is d.
1. What is the payoff/utility of player 1 if both players decide to defect all the time? Assume 8 = 0.59.
Write at least 3 digits after the decimal place.
2. What is the payoff/utility of player 1 if both players decide to cooperate all the time? Assume d = 0.65.
Write at least 3 digits after the decimal place.
3. Find the minimum value of 5 for which player 1 will have no incentive to defect on the first stage, assuming player 1 and 2 both are playing grim
trigger strategy.
Write at least 3 digits after the decimal place.

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