Consider the infinite repeated two-player game where at each stage the play- ers play the non-zero-sum game given by A В A (5,5) (0,7) B (7,0) | (2,2) (a) Consider the following strategies: SA: always play A. SB: always play B. • St: play A on the first stage, thereafter copy what the other player did in the preceding stage. Suppose that the total payoff involves a discount factor 8, and that both players are restricted to the pure strategies sA, 8B, and sr. Determine the set of d for which (sT, sT) is a Nash equilibrium. (b) Use the one stage deviation principle to determine whether the pair (ST, ST) is a subgame perfect Nash equilibrium for some range of val- ues of §.

Consider the infinite repeated two-player game where at each stage the play- ers play the non-zero-sum game given by A В A (5,5) (0,7) B (7,0) | (2,2) (a) Consider the following strategies: SA: always play A. SB: always play B. • St: play A on the first stage, thereafter copy what the other player did in the preceding stage. Suppose that the total payoff involves a discount factor 8, and that both players are restricted to the pure strategies sA, 8B, and sr. Determine the set of d for which (sT, sT) is a Nash equilibrium. (b) Use the one stage deviation principle to determine whether the pair (ST, ST) is a subgame perfect Nash equilibrium for some range of val- ues of §.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.3P

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