Externalities and Renegotiations in Three-Player Coalitional Bargaining

Abstract

This paper proposes a new solution concept to three-player coalitional bargaining problems. The coalitional bargaining problem is modeled as a dynamic non-cooperative game in which players make conditional or unconditional offers, coalitions continue to negotiate as long as there are gains from trade, and coalitions may create positive or negative externalities. The theory yields a unique stationary subgame perfect Nash equilibrium outcome - the coalitional bargaining value-that has an intuitive economic interpretation using endogenous outside options. Interestingly, this solution can either be the Nash bargaining solution, for games where the worth of all pairwise coalition is less than a third of the grand coalition value; the Shapley value, for games where the sum of the value created by all pairwise coalitions is greater than the grand coalition value; or the nucleolus, for games where only the 'natural coalition' among two 'natural partners' creates significant value, and those where only the two pairwise coalitions including a 'pivotal player' create significant value.

Keywords: Coalitional bargaining, uniqueness, externalities, conditional and unconditional offers

JEL Classification: C71, C72, C78, D62