Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 1 000 2 R M 3 1 Player's payoff 0 player 2 payoff O player 3's payoff о 1 1 9 010 221 E 000 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.

Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 1 000 2 R M 3 1 Player's payoff 0 player 2 payoff O player 3's payoff о 1 1 9 010 221 E 000 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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