Consider a model that is "in between" the ultimatum game and the Rubinstein bargaining model. Players 1 and 2 have to divide a pie. The whole pie is worthv1to player 1 andv2to player 2.

Player 1 makes a proposal first, which is a numberxin [0,1]. Player 2 can accept the offer, in which case the payoffs of players 1 and 2 arev1(1-x)andv2x, respectively. Otherwise, player 2 rejects the offer and then can make a new proposalx'to player 1. If player 1 accepts, the payoffs of players 1 and 2 ared1v1x'andd2v2(1-x'), respectively, whered1andd2are numbers in (0,1). If player 1 rejects the offerx', the players payoffs are (0,0).

Suppose the players play a subgame perfect Nash equilibrium of this game. Whatx'will player 2 offer in any subgame after player 2 rejects the first offer?