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. Under the strong version of the assumption, we characterize the essentially unique subgame perfect equilibrium path, which involves considerable delay and efficiency loss. We give different interpretations of the assumption. The assumption can also be weakened under the interpretation of loss aversion. We provide a sufficent condition under which the feature of the equilibrium from strong assumption remains. JEL-codes: C72, C78.