CARESS Working Paper 99-12 A Theory of Negotiations and Formation of Coalitions

This paper proposes a new solution concept to three-player coalitional bargaining problems where the underlying economic opportunities are described by a partition function. This classic bargaining problem is modeled as a dynamic non-cooperative game in which players make conditional or unconditional offers, and coalitions continue to negotiate as long as there are gains from trade. The theory yields a unique stationary perfect equilibrium outcome—the negotiation value—and provides a unified framework that selects an economically intuitive solution and endogenous coalition structure. For such games as pure bargaining games the negotiation value coincides with the Nash bargaining solution, and for such games as zero-sum and majority voting games the negotiation value coincides with the Shapley value. However, a novel situation arises where the outcome is determined by pairwise sequential bargaining sessions in which a pair of players forms a natural match. In addition, another novel situation exists where the outcome is determined by one pivotal player bargaining unconditionally with the other players, and only the pairwise coalitions between the pivotal player and the other players can form. keywords: Coalitional bargaining, subgame perfect equilibrium, existence, uniqueness, partition functions, externalities, conditional and unconditional offers. ∗Comments welcome. I would to thank Kenneth Kavajecz, George Mailath, Steven Matthews, and Andrew Postlewaite for helpful comments. Correspondence: Finance Dept., The Wharton School, 2300 Steinberg Hall-Dietrich Hall, Philadelphia, PA 19104. E-mail: [email protected]. Tel: (215) 898-3477. Web page: http://finance.wharton.upenn.edu/ ̃gomes.