Problem 4: Consider an infinitely repeated game, where the base game is thefollowing 2-person 2x2 game:AA0,010, 10S1: choose A alwaysS2: choose B alwaysB10, 100,0Assume both players discount the future at the same rate of r, 0 < r < 1.Limiting each player's strategies to the following six possibilities,S3: Choose A then mimic the other player's previous choiceS4: Choose B, then mimic the other player's previous choiceS5: Choose A, then choose the opposite of the other player's previous choiceS6: Choose B, then choose the opposite of the other player's previous choicea. present the strategic form of this game,b. identify all pure-strategy Nash equilibriac. does repetition with these strategies "solve" the coordination dilemma thatconfronts the players in the single play of the above game.

Given: Base game 2*2 games with 2 people. Game is infinitely repeated. Both the players discount…

Problem 4: Consider an infinitely repeated game, where the base game is the following 2-person 2x2 game: A B A 0,0 10, 10 S1: choose A always S2: choose B always B 10, 10 0,0 Assume both players discount the future at the same rate of r, 0

Problem 4: Consider an infinitely repeated game, where the base game is the following 2-person 2x2 game: A B A 0,0 10, 10 S1: choose A always S2: choose B always B 10, 10 0,0 Assume both players discount the future at the same rate of r, 0

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Question

Problem 4: Consider an infinitely repeated game, where the base game is the
following 2-person 2x2 game:
A
A
0,0
10, 10
S1: choose A always
S2: choose B always
B
10, 10
0,0
Assume both players discount the future at the same rate of r, 0 < r < 1.
Limiting each player's strategies to the following six possibilities,
S3: Choose A then mimic the other player's previous choice
S4: Choose B, then mimic the other player's previous choice
S5: Choose A, then choose the opposite of the other player's previous choice
S6: Choose B, then choose the opposite of the other player's previous choice
a. present the strategic form of this game,
b. identify all pure-strategy Nash equilibria
c. does repetition with these strategies "solve" the coordination dilemma that
confronts the players in the single play of the above game.

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