Bargaining with History Dependent Preferences

We study perfect information bilateral bargaining game with an infinite alternating-offers procedure, in which we add an assumption of history dependent preference. A player will devalue a share which gives her strictly lower discounted utility than what she was offered in earlier stages of the bargaining, namely, a ``worse off'' outcome. In a strong version of the assumption, each player prefers impasse to any ``worse off'' outcome. We characterize the essentially unique subgame perfect equilibrium path under the assumption. The equilibrium entails considerable delay and efficiency loss. As the players become infinitely patient, the efficiency loss goes to one half, and the equilibrium share goes to Nash solution. The assumption can also be weakened. We provide a sufficient condition on the extent of devaluation under which the feature of the equilibrium from strong assumption remains