Two individuals are bargaining over how to divide a prize of value V. The prize is...

 

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Two individuals are bargaining over how to divide a prize of value V. The prize is such that its value declines over time, so that it is worth V in period 1, dV in period 2, and so on. Bargaining proceeds in stages as follows: Player 1 makes an offer of a share to Player 2, who can then either Accept the offer or Reject the offer. If Accept, then 2 receives the offer as payoff and 1 receives what is left, and the game ends. If 2 Rejects, then a new stage begins, the value of the prize reduces by factor 6, and the players switch places. Player 2 makes an offer and 1 can Accept or Reject. In the last stage of the game, one player makes an offer ends which the other Accepts or Rejects. If Reject, then payoffs are (0,0) and the game ends. Solve the game if the number of periods is 1, 2, or 3. Note that this means solving 3 different games. Two individuals are bargaining over how to divide a prize of value V. The prize is such that its value declines over time, so that it is worth V in period 1, dV in period 2, and so on. Bargaining proceeds in stages as follows: Player 1 makes an offer of a share to Player 2, who can then either Accept the offer or Reject the offer. If Accept, then 2 receives the offer as payoff and 1 receives what is left, and the game ends. If 2 Rejects, then a new stage begins, the value of the prize reduces by factor 6, and the players switch places. Player 2 makes an offer and 1 can Accept or Reject. In the last stage of the game, one player makes an offer ends which the other Accepts or Rejects. If Reject, then payoffs are (0,0) and the game ends. Solve the game if the number of periods is 1, 2, or 3. Note that this means solving 3 different games.