Multilateral Negotiations and Formation of Coalitions

This paper studies multilateral negotiations among n players in an environment where there are externalities and contracts forming coalitions can be written and renegotiated. The negotiation process is modeled as sequential game of offers and counteroffers, and the study focus on the stationary subgame perfect equilibria, which jointly determines both the expected value of players, and the Markov state transition probability that encodes the path of coalition formation. The existence of equilibria is established, and Pareto efficiency is guaranteed if the grand coalition is efficient, despite the existence of externalities. The equilibria correspond to the solutions of a certain mixed nonlinear complementarity problem, a well-known problem in mathematical programming, which allow us to numerically obtain solutions using proven algorithms. Also, for almost all games (except in a set of measure zero) the equilibrium is locally unique and stable, and the number of equilibria is finite and odd. Global uniqueness does not hold in general (a public good provision example has seven equilibria) but a general sufficient condition for global uniqueness is derived. Using this sufficient condition, we show that there is a globally unique equilibrium in three-player superadditive games. Comparative statics analysis can be easily carried on using standard calculus tools, and some new insights emerge from the investigation of the classic apex and quota games.