Bargaining Equilibrium in a Non-Stationary Environment

In this paper we study an alternating-offers bargaining model in which the set of possible utility pairs evolves through time in a non-stationary, but smooth manner. In general there exists a multiplicity of subgame perfect equilibria. However, we show that in the limit as the time interval between two consecutive offers becomes arbitrarily small, there exists a unique subgame perfect equilibrium. Furthermore, and more importantly, we derive a powerful characterization of the unique (limiting) subgame perfect equilibrium payoffs, which should prove especially useful in applications. We then explore the circumstances under which Nash’s bargaining solution implements this bargaining equilibrium. Finally, we extend our results to the case when the players have time-varying inside options. JEL Classification Nos: C78, D43.