3. Two players play the following normal form game. Left Middle Right 1\2 Left 4,2 3,3 1,2 Middle 3,3 5,5 2,6 Right 2,1 6,2 3,3 Suppose that there is a probability p that the game continues next period and a probability (1 - p) that it ends. What is the threshold p* such that when p p* (Middle, Middle) is sustainable as a subgame perfect equilibrium by grim trigger strategies, but when p < p* playing Middle in all periods is not a best response? [Here the grim strategy is: play Middle if the play in all previous periods was (Middle, Middle); play Right otherwise.] a) 1/2; b) 1/3; c) 1/4; d) 2/5.

3. Two players play the following normal form game. Left Middle Right 1\2 Left 4,2 3,3 1,2 Middle 3,3 5,5 2,6 Right 2,1 6,2 3,3 Suppose that there is a probability p that the game continues next period and a probability (1 - p) that it ends. What is the threshold p* such that when p p* (Middle, Middle) is sustainable as a subgame perfect equilibrium by grim trigger strategies, but when p < p* playing Middle in all periods is not a best response? [Here the grim strategy is: play Middle if the play in all previous periods was (Middle, Middle); play Right otherwise.] a) 1/2; b) 1/3; c) 1/4; d) 2/5.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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