a) Solve for the game's subgame perfect equilibrium. Make sure to list what offer will be made in each period, in what period (if any) an offer will be accepted, and how the surplus is divided. b) Now suppose Player 2 has an option to pay a bribe of $X at the beginning of Period 1, which would increase the amount they'd receive in Period 3 if the offer was rejected to $20. Assume no other bargaining aspects are affected by the potential bribe. Given a discount factor of s = 0.7, what's the maximum bribe they'd be willing to pay?

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter17: Making Decisions With Uncertainty
Section: Chapter Questions
Problem 17.5IP
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The question is an two-part economics applied theory exercise. 

Period 1: Player 1 proposes sı to keep and (1-s1) for Player 2 to accept. If Player 2 accepts the
offer, the game is over and the proposed shares are paid out. If Player 2 rejects the Period 1 offer,
the game proceeds to Period 2.
Period 2: Player 2 proposes s2 for Player 1 to keep and (1-s2) for themselves. If Player 1 accepts,
the game is over. If Player 1 rejects, the game goes to a third and final round.
Period 3: Player 1 proposes s3 to keep and (1-s3) for Player 2 to accept. If Player 2 accepts the
offer, the game is over and the proposed shares are paid out. If Player 2 rejects the Period 3 offer,
both players immediately receive $10. The remaining $80 is lost to arbitrators in the court system.
In this sequential bargaining problem, the discount factor is 8 = 0.7.
Transcribed Image Text:Period 1: Player 1 proposes sı to keep and (1-s1) for Player 2 to accept. If Player 2 accepts the offer, the game is over and the proposed shares are paid out. If Player 2 rejects the Period 1 offer, the game proceeds to Period 2. Period 2: Player 2 proposes s2 for Player 1 to keep and (1-s2) for themselves. If Player 1 accepts, the game is over. If Player 1 rejects, the game goes to a third and final round. Period 3: Player 1 proposes s3 to keep and (1-s3) for Player 2 to accept. If Player 2 accepts the offer, the game is over and the proposed shares are paid out. If Player 2 rejects the Period 3 offer, both players immediately receive $10. The remaining $80 is lost to arbitrators in the court system. In this sequential bargaining problem, the discount factor is 8 = 0.7.
a) Solve for the game's subgame perfect equilibrium. Make sure to list what
offer will be made in each period, in what period (if any) an offer will be
accepted, and how the surplus is divided.
b) Now suppose Player 2 has an option to pay a bribe of $X at the beginning of
Period 1, which would increase the amount they'd receive in Period 3 if the
offer was rejected to $20. Assume no other bargaining aspects are affected by
the potential bribe. Given a discount factor of s = 0.7, what's the maximum
bribe they'd be willing to pay?
Transcribed Image Text:a) Solve for the game's subgame perfect equilibrium. Make sure to list what offer will be made in each period, in what period (if any) an offer will be accepted, and how the surplus is divided. b) Now suppose Player 2 has an option to pay a bribe of $X at the beginning of Period 1, which would increase the amount they'd receive in Period 3 if the offer was rejected to $20. Assume no other bargaining aspects are affected by the potential bribe. Given a discount factor of s = 0.7, what's the maximum bribe they'd be willing to pay?
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