Holdup: Consider an ultimatum game (T = 1 bargaining game) in which before player 1 makes his offer to player 2, player 2 can invest in the size of the pie. If player 2 chooses a low level of investment (L) then the size of the pie is small, equal to vL, while if player 2 chooses a high level of investment (H) then the size of the pie is large, equal to VH. The cost to player 2 of choosing L is c1, while the cost of choosing H is CH. Assume that ví > V1 > 0, cH > CL > 0, and vH - CH > vL = CL· What is the unique subgame-perfect equilibrium of this game? Is it Pareto optimal? b. Can you find a Nash equilibrium of the game that results in an outcome that is better for both players as compared to the unique subgame- perfect equilibrium?

Holdup: Consider an ultimatum game (T = 1 bargaining game) in which before player 1 makes his offer to player 2, player 2 can invest in the size of the pie. If player 2 chooses a low level of investment (L) then the size of the pie is small, equal to vL, while if player 2 chooses a high level of investment (H) then the size of the pie is large, equal to VH. The cost to player 2 of choosing L is c1, while the cost of choosing H is CH. Assume that ví > V1 > 0, cH > CL > 0, and vH - CH > vL = CL· What is the unique subgame-perfect equilibrium of this game? Is it Pareto optimal? b. Can you find a Nash equilibrium of the game that results in an outcome that is better for both players as compared to the unique subgame- perfect equilibrium?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.8P

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