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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0f334c6-c73d-428b-8d60-f5c8db4e6ca2%2F55802ba7-d722-4c46-85ee-09c994226215%2Fud2mld.png&w=3840&q=75)
Transcribed Image Text: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?
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