4. Consider the following variant of the Prisoner's Dilemma game: Player 1 is unsurewhether Player 2 is "nice" or "selfish", while Player 2 knows Player 1's preferences.Further suppose that Player 1's preferences depend on whether Player 2 is niceor selfish. Specifically, suppose that there is a probability p that Player 2 is "selfish",in which case the game is given as follows.Game with Selfish Player 2Player1/Player 2Cooperate (C)Don't Cooperate (D)Cooperate (C)4, 40, 6Don't Cooperate (D)6, 02, 2And Player 2 is "nice" with probability 1-p, in which case the following gameresults.Game with Nice Player 2Player1/Player 2Cooperate (C)Don't Cooperate(D)2, 4Cooperate (C)6, 6Don't Cooperate (D)4, 00, 2[Note that C = cooperate (with each other) and D = don't cooperate or defect).a) Write the extensive form of this game. How many strategies does eachplayer have in this game?b) For what values of p (if any) is it a Bayes-Nash equilibrium for Player 1 toplay D in response to D by both types of Player 2? Explain your answer.c) For what values of p (if any) is it a Bayes-Nash equilibrium for Player 1 toplay C in response to D bv a selfish Player 2 and C by a nice Player 2?Explain your answer.

Given information Probability of player 2 is selfish=p Probability of player 2 is nice=1-p Pay off…

4. Consider the following variant of the Prisoner's Dilemma game: Player 1 is unsure whether Player 2 is "nice" or "selfish", while Player 2 knows Player 1's preferences. Further suppose that Player 1's preferences depend on whether Player 2 is nice or selfish. Specifically, suppose that there is a probability p that Player 2 is "selfish", in which case the game is given as follows. Game with Selfish Player 2 Player1/Player 2 Cooperate (C) Don't Cooperate (D) Cooperate (C) 4, 4 0,6 Don't Cooperate (D) 6, 0 2, 2 And Player 2 is "nice" with probability 1-p, in which case the following game results.

4. Consider the following variant of the Prisoner's Dilemma game: Player 1 is unsure whether Player 2 is "nice" or "selfish", while Player 2 knows Player 1's preferences. Further suppose that Player 1's preferences depend on whether Player 2 is nice or selfish. Specifically, suppose that there is a probability p that Player 2 is "selfish", in which case the game is given as follows. Game with Selfish Player 2 Player1/Player 2 Cooperate (C) Don't Cooperate (D) Cooperate (C) 4, 4 0,6 Don't Cooperate (D) 6, 0 2, 2 And Player 2 is "nice" with probability 1-p, in which case the following game results.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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Consider a repeated game with the following stage game: Player 1 O O O Cooperate Not Cooperate This game is repeated T-120 times, and t each period both players must choose their actions simultaneously. The players are deciding whether or not to cooperate specifically, whether or not to follow this cooperation strategy: r≤ 3 S|S|AW|N N|H "Each player will play cooperate as long as no one has played Not Cooperate before. If someone has played Not Cooperate before, then each player will play Not Cooperate forever." rs 5 rs Player 2 In this case, cooperation will be possible if the interest rate r is Not Cooperate 5,15 10, 10 None of the above Cooperate 12, 12 15,5
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