Multilateral Negotiations and Formation of Coalitions
AbstractThis 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.
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Bibliographic InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2001 with number 224.
Date of creation: 01 Apr 2001
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coalitional bargaining; externalities; renegotiation;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D62 - Microeconomics - - Welfare Economics - - - Externalities
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-05-02 (All new papers)
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- Montero, Maria, 2006. "Noncooperative foundations of the nucleolus in majority games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 380-397, February.
- Westermark, Andreas, 2003. "Bargaining, binding contracts, and competitive wages," Games and Economic Behavior, Elsevier, vol. 43(2), pages 296-311, May.
- Montero, M.P., 2001. "The Nucleolus as a Consistent Power Index in Noncooerative Majority Games," Discussion Paper 2001-39, Tilburg University, Center for Economic Research.
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