Question

Consider the following bargaining game in which two players are trying to share a cake of size 1. Player 1 offers ri e [o, 1jand player 2 either accepts (Y) of rejects (N): If player 2 accepts player 1 receives a payoff of ri and player 2 receives 1-1. If player 2 rejects, then player 2 moves again to offer 72 [0, 1] to which player 1 responds by either accepting (Y) or rejecting (N): If player 1 accepts player 1 and 2's payoffs are δ (1-12) and δΧ2 respectively, where δ e (0,1) is the common discount factor for the players. If player i rejects the offer then an arbitrator terminates the bargaining process and gives player 1 a share y and player 2 the rest which, because of discounting, players value as δ2y and δυ y). Find the SPE of this game.

Answer 1

If the both the players agree to get half-half of the cake. It�s beneficial for them i.e, P1 of 2 (2nd option) or P2 of 2 (2nd option) Though, if they do not agree for the above option, They can even share the acke among themselves as pieces i./e Pi of 1 (1st portion) or P2 of 1 (1^st portion). The extensive form of the two players bargaining game. Here P1, P2 and P3 0represente the periods and the (S1, - S1), (1/2, 1/2), (S2, 1-S2) and (1/3, 1/3) are slices of the cake. It�s clear from the diagram. Finally, if both of the players do not agree for both of the above conditions, then they have to hire the orbitrator.