Question 6. (15 Points)

Consider the following ultimatum game. In Stage 1, the proposer chooses a share of $1 to offer to the responder. The share can be any number between 0 and 1 (including 0 and 1). After observing the proposer's decision, the responder may choose to accept or reject. If the responder accepts, the proposer keeps and the responder receives . If the responder rejects, both players receive 0. Assume that the responder always accepts when she is indifferent between accepting and rejecting.

Suppose that both the proposer (Player ) and the responder (Player ) exhibit inequity aversion as specified in the model of Fehr and Schmidt (1999), with and ( and are the parameters for player ; and are the parameters for player ). Suppose these preferences are commonly known to both players. Use backward induction to solve the subgame perfect Nash equilibrium.