Problem
Consider the following Rubinstein alternating-offer bargaining game that lasts for three periods. Two players bargain over how to share the value of a pig. The pig is worth 1 in period 1. This pig grows, and it is worth 2 in period 2, and then worth 3 in period 3. The discount factor for both players is given by δ. In this alternating-offer bargaining game, player 1 makes the offer in period 1. Then player 2 makes the offer in period 2, and player 1 makes the offer in period 3. If no agreement is reached by the end of period 3, the pig runs away and both players get 0. Once a player makes an offer, the other player can accept or reject the offer. Accepting the offer ends the game, while rejecting the offer leads the game to the next period.
1. Suppose that there is no discounting (i.e., δ = 1). Find the subgame-perfect equilibrium in this game.
2. Suppose that δ = 0.5. Find the subgame-perfect equilibrium in this game.