This paper analyses properties of games modelling multilateral negotiations leading to the formation of coalitions in an environment with widespread externalities. The payo¤ generated by each coalition is determined by a set of exogenous parameters. We show that in almost all games, except in a set of measure zero of the parameter space, the Markov perfect equilibrium is locally unique and stable, and comparative statics analysis are well-de ned and can be performed using standard calculus tools. Global uniqueness does not hold in general, but the number of equilibria is nite and odd. In addition, a su¢ cient condition for global uniqueness is derived, and using this su¢ cient condition we show that there is a globally unique equilibrium in three-player superadditive games. jel: C71, C72, C78, D62 keywords: Coalitional bargaining, externalities, multilateral negotiations. I would like to thank seminar participants at Princeton University, University of Pennsylvania, and the World Congress of the Econometric Society. Address: Washington University in St. Louis, One Brookings Drive, Campus Box 1133, MO 63130-4899. E-mail: email@example.com. Tel: (314) 935-4569.