c) Consider the centipede game which illustrates the situation where it is mutually beneficial for all players to stay in a relationship while a player would like to exit the relationship if they know that the other player will exit in the next day. Note that the fourth day is the choice for Player 2 to move and choose either o or 0. Use the logic of backwards induction to find the subgame perfect Nash equilibrium of the game in Figure 1. Figure 1: The Centipede Game 2 d (1 (64,16) D d (2,8) (4,2) (164) 0 (8,32)

c) Consider the centipede game which illustrates the situation where it is mutually beneficial for all players to stay in a relationship while a player would like to exit the relationship if they know that the other player will exit in the next day. Note that the fourth day is the choice for Player 2 to move and choose either o or 0. Use the logic of backwards induction to find the subgame perfect Nash equilibrium of the game in Figure 1. Figure 1: The Centipede Game 2 d (1 (64,16) D d (2,8) (4,2) (164) 0 (8,32)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.7P

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