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Problem 2. Below-Nash punishment. Consider an infinite repeated game where the stage game is given as follows: Player 2 L C R T 10,10 3, 15 0,7 Player 1 M 15,3 7,7 -4,5 B 7,0 5,-4 -15, 15 (a) Find all pure-strategy Nash equilibrium of the stage game. (b) Using Folk Theorem, show that there exists a discount factor 8 < 1 such that a pure strategy subgame perfect equilibrium in which the players play strategy profile TL in every period along the equilibrium path. (c) Prove that off-equilibrium path punishment of MR, TC, TC,... for player 1, and BC, ML, ML,... for player 2 is a support for equilibrium.

Problem 2. Below-Nash punishment. Consider an infinite repeated game where the stage game is given as follows: Player 2 L C R T 10,10 3, 15 0,7 Player 1 M 15,3 7,7 -4,5 B 7,0 5,-4 -15, 15 (a) Find all pure-strategy Nash equilibrium of the stage game. (b) Using Folk Theorem, show that there exists a discount factor 8 < 1 such that a pure strategy subgame perfect equilibrium in which the players play strategy profile TL in every period along the equilibrium path. (c) Prove that off-equilibrium path punishment of MR, TC, TC,... for player 1, and BC, ML, ML,... for player 2 is a support for equilibrium.

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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Problem 2. Below-Nash punishment. Consider an infinite repeated game where the stage game is given as follows: Player 2 L C R T 10,10 3, 15 0,7 Player 1 M 15,3 7,7 -4,5 B 7,0 5,-4 -15, 15 (a) Find all pure-strategy Nash equilibrium of the stage game. (b) Using Folk Theorem, show that there exists a discount factor 8 < 1 such that a pure strategy subgame perfect equilibrium in which the players play strategy profile TL in every period along the equilibrium path. (c) Prove that off-equilibrium path punishment of MR, TC, TC,... for player 1, and BC, ML, ML,... for player 2 is a support for equilibrium.
Transcribed Image Text:Problem 2. Below-Nash punishment. Consider an infinite repeated game where the stage game is given as follows: Player 2 L C R T 10,10 3, 15 0,7 Player 1 M 15,3 7,7 -4,5 B 7,0 5,-4 -15, 15 (a) Find all pure-strategy Nash equilibrium of the stage game. (b) Using Folk Theorem, show that there exists a discount factor 8 < 1 such that a pure strategy subgame perfect equilibrium in which the players play strategy profile TL in every period along the equilibrium path. (c) Prove that off-equilibrium path punishment of MR, TC, TC,... for player 1, and BC, ML, ML,... for player 2 is a support for equilibrium.
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