prove that the following strategy profile is a Nash equilibrium: For any 0 < x ≤1, player 1 offers x to player 2, player 2 accepts any offer greater than or equal to x and rejects any offer smaller than x. Is this strategy profile a subgame perfect equilibrium as well? Briefly explain why.

prove that the following strategy profile is a Nash equilibrium: For any 0 < x ≤1, player 1 offers x to player 2, player 2 accepts any offer greater than or equal to x and rejects any offer smaller than x. Is this strategy profile a subgame perfect equilibrium as well? Briefly explain why.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.6P

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Question

prove that the following strategy profile is a Nash equilibrium:
For any 0 < x ≤1, player 1 offers x to player 2, player 2 accepts any offer greater than or
equal to x and rejects any offer smaller than x.
Is this strategy profile a subgame perfect equilibrium as well? Briefly explain why.

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