24. Two individuals play the following infinitely repeated prisoner's dilemma game:Player ACooperateDefectPlayer BCooperate3,57,0Defect0,61, 1Assume that both players discount future payoffs at rate 8<1.(a) If both players play 'cooperate' every period, then what are their total payoffs? (b) What would be their payoffs if they decide to defect forever?(c) If both players play the 'Grim Trigger' strategy then what discount factor (8≥ 0) isneeded to support this as a Nash equilibrium?(d) Now consider what happens when both players play 'Tit-for-Tat'.(i)(ii)(iii)What are the payoffs from playing Tit-for-Tat when the other player does?Suppose >1/6, what is best way to exploit a player playing Tit-for-Tat?(Hint: A payoff every 2 periods is discounted at rate 8²)Is it ever possible to sustain cooperation if one of the players uses Tit-for-Tat?

There are two player A & B .Strategy Set (A) = Strategy Set (B ) = { Cooperate , Defect }Payoffs…

. Two individuals play the following infinitely repeated prisoner's dilemma game: Player A Cooperate Defect Player B Cooperate 3,5 7,0 Defect 0,6 1, 1 Assume that both players discount future payoffs at rate 6<1. (a) If both players play 'cooperate' every period, then what are their total payoffs?

. Two individuals play the following infinitely repeated prisoner's dilemma game: Player A Cooperate Defect Player B Cooperate 3,5 7,0 Defect 0,6 1, 1 Assume that both players discount future payoffs at rate 6<1. (a) If both players play 'cooperate' every period, then what are their total payoffs?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.6P

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