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A Theory of Negotiation and Formation of Coalition

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  • Armando Gomes

Abstract

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 provide 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.

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Paper provided by University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences in its series CARESS Working Papres with number 99-12.

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Handle: RePEc:wop:pennca:99-12

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  1. Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
  2. Hart, Oliver & Moore, John, 1990. "Property Rights and the Nature of the Firm," Journal of Political Economy, University of Chicago Press, vol. 98(6), pages 1119-58, December.
  3. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  4. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667 Elsevier.
  5. Ray, Debraj & Vohra, Rajiv, 1997. "Equilibrium Binding Agreements," Journal of Economic Theory, Elsevier, vol. 73(1), pages 30-78, March.
  6. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  7. Debraj Ray & Rajiv Vohra, 1998. "A Theory of Endogenous Coalition Structures," Working Papers 98-1, Brown University, Department of Economics, revised Jan 1998.
  8. Moldovanu, Benny, 1992. "Coalition-proof nash equilibria and the core in three-player games," Games and Economic Behavior, Elsevier, vol. 4(4), pages 565-581, October.
  9. Chatterjee, Kalyan & Bhaskar Dutta & Debraj Ray & Kunal Sengupta, 1993. "A Noncooperative Theory of Coalitional Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 60(2), pages 463-77, April.
  10. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  11. Sutton, John, 1986. "Non-cooperative Bargaining Theory: An Introduction," Review of Economic Studies, Wiley Blackwell, vol. 53(5), pages 709-24, October.
  12. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  13. Armando Gomes & Sergiu Hart & Andreu Mas-Colell, 1997. "Finite Horizon Bargaining and the Consistent Field," Game Theory and Information 9705003, EconWPA.
  14. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  15. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  16. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
  17. Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, vol. 19(2), pages 151-179, May.
  18. Bloch, Francis, 1996. "Sequential Formation of Coalitions in Games with Externalities and Fixed Payoff Division," Games and Economic Behavior, Elsevier, vol. 14(1), pages 90-123, May.
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Cited by:
  1. Kyle Bagwell & Robert W. Staiger, 2002. "Multilateral trade negotiations, bilateral opportunism and the rules of GATT/WTO," Discussion Papers 0102-37, Columbia University, Department of Economics.
  2. Tobias Lindqvist & Johan Stennek, 2005. "The Insiders’ Dilemma: An Experiment on Merger Formation," Experimental Economics, Springer, vol. 8(3), pages 267-284, September.
  3. Lindqvist, Tobias & Stennek, Johan, 2005. "The Insiders' Dilemma: An Experiment on Merger Formation," CEPR Discussion Papers 5016, C.E.P.R. Discussion Papers.
  4. Nikitas Konstantinidis, 2008. "Gradualism and uncertainty in international union formation: The European Community’s first enlargement," The Review of International Organizations, Springer, vol. 3(4), pages 399-433, December.

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