A Continuous Time Model of Bilateral Bargaining

This paper presents a continuous time model of bilateral bargaining in which the players relative bargaining power evolves as a di¤usion process. The model has a unique equilibrium, in which players reach an immediate agreement. The playerspayo¤s are characterized by a system of ordinary di¤erential equations. Closed-form solutions to these equations are available when relative bargaining power evolves as a Brownian motion with constant drift and constant volatility. The equilibrium of the continuous time model corresponds to the limiting subgame perfect equilibrium of a discrete time bargaining game, when players can make o¤ers arbitrarily frequently. The paper also presents two applications of the baseline model featuring delays and ine ¢ ciencies. I am indebted to Faruk Gul, Wolfgang Pesendorfer and Sylvain Chassang for advice, encouragement and support. For helpful comments I also thank Dilip Abreu, Roland Benabou, Stephen Morris, Yuli