Gradualism in Bargaining and Contribution Games∗

We model bargaining situations in which parties have the option to terminate the negotiation, resulting in a termination outcome that depends on the offers made in the negotiation phase. The key features of the model are that 1) making a concession in the negotiation phase increases the other party’s termination option payoff and 2) the termination outcome induces an efficiency loss as compared with a negotiated agreement. The main Þnding is that the mere threat of termination forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which partial projects can be implemented. Our Þndings are contrasted with those appearing in the literature. Journal of Economic Literature ClassiÞcation Numbers: C72, C78, D60. ∗We thank David Frankel, George Mailath, Steve Matthews, Ariel Rubinstein, Jozsef Sakovics, Jean Tirole, Jörgen Weibull, Yoram Weiss, and seminar participants at Tel Aviv University, Séminaire Fourgeaud (Paris), CEPR Summer meeting at Gerzensee, 7 World Congress of the Econometric Society Tokyo 1995, MIT-Harvard, Princeton, Mannheim, LSE, SED conference 1999, for helpful comments. †C.E.R.A.S.-E.N.P.C., C.N.R.S. (URA 2036), 28 Rue des Saints-Pères, 75007 Paris, France, [email protected]. ‡C.E.R.A.S., Paris, (C.N.R.S. URA 2036), and U.C.L, U.K., [email protected].