Answered: 1) Consider the following variant of…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

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$1) Consider the following variant of the prisoner's dilemma with altruistic preferences. For simplicity, I'm adding 15 to the payoffs of the baseline normal form representation of the game we describe in class which results in the following: Player I\ Player 2 Cooperate Non-Cooperate Cooperate 8.8 0,15 Non Cooperate 15,0 14,14 Assume now that the players are not “selfish”; rather the preference of each player i are represented by the payoff (utility) function m; (a) + ßm; (a) where mi(a) is the payoff received by player i when the strategy profile is a, j is the other player, and ß is a given non-negative number. Player 1's payoff to the strategy profile (Cooperate, Cooperate), for example, is 8+8ß. A) Assume ß = 1. Write the normal form of the game. Is this game a prisoner's dilemma? What is the Nash equilibria of the game? B) Find the range of values of ß for which the resulting game is the prisoner's dilemma.$

Transcribed Image Text:1) Consider the following variant of the prisoner's dilemma with altruistic preferences. For simplicity, I'm adding 15 to the payoffs of the baseline normal form representation of the game we describe in class which results in the following: Player I\ Player 2 Cooperate Non-Cooperate Cooperate 8.8 0,15 Non Cooperate 15,0 14,14 Assume now that the players are not “selfish”; rather the preference of each player i are represented by the payoff (utility) function m; (a) + ßm; (a) where mi(a) is the payoff received by player i when the strategy profile is a, j is the other player, and ß is a given non-negative number. Player 1's payoff to the strategy profile (Cooperate, Cooperate), for example, is 8+8ß. A) Assume ß = 1. Write the normal form of the game. Is this game a prisoner's dilemma? What is the Nash equilibria of the game? B) Find the range of values of ß for which the resulting game is the prisoner's dilemma.

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