3) Assume that two players (Player 1 and Player 2) bargain on how to divide $100...

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3) Assume that two players (Player 1 and Player 2) bargain on how to divide $100 over the course of three periods. Suppose they play the following bargaining game: Period 1: Player 1 proposes s/ to keep and (1-5) 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 (1-52) 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 (1-53) 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) (10 points) 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) (5 points) 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 8 = 0.7, what's the maximum bribe they'd be willing to pay? 3) Assume that two players (Player 1 and Player 2) bargain on how to divide $100 over the course of three periods. Suppose they play the following bargaining game: Period 1: Player 1 proposes s/ to keep and (1-5) 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 (1-52) 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 (1-53) 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) (10 points) 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) (5 points) 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 8 = 0.7, what's the maximum bribe they'd be willing to pay?

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Solving the Subgame Perfect Equilibrium SPE We will use backward induction to solve for the SPE starting from the last period and working our way back ... View the full answer