Unique Equilibria in the Rubinstein Bargaining Model when the Payoff Set is Non-Convex

I give necessary and su¢ cient conditions for the uniqueness of the equilibrium in a wide class of Rubinstein bargaining models. The requirements encompass a class of non-convex or disconnected payo¤ sets with discontinuous Pareto frontiers. The equilibrium of the non-cooperative game is unique if the objective function of the corresponding Nash-bargaining game has a unique maximum. I extend the analysis to games where the time between o¤ers is not constant. Keywords: Bargaining JEL Classi…cation Number: C78 Wolfgang R. Köhler IEW. University of Zürich, Winterthurerstrasse 30, 8006 Zürich, Switzerland (E-mail: [email protected]) I would like to thank Thomas Jeitschko, Chris Laincz, Christoph Nitzsche, Huseyin Yildirim, and especially Curtis Taylor.