Exercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R 1 player I's payoff 000 2 O player 2's payoff O player 3's payoff M 3 b 0 1 1 010 1 0 1 2 221 2 0 000 (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 R 1 player I's payoff 000 2 O player 2's payoff O player 3's payoff M 3 b 0 1 1 010 1 0 1 2 221 2 0 000 (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.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.1P
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