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A Theory of Negotiations and Formation of Coalitions

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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 Wharton School Rodney L. White Center for Financial Research in its series Rodney L. White Center for Financial Research Working Papers with number 21-99.

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Handle: RePEc:fth:pennfi:21-99
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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  2. 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.
  3. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," 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 7, pages 179-225 Elsevier.
  4. Armando Gomes & Sergiu Hart & Andreu Mas-Colell, 1997. "Finite horizon bargaining and the consistent field," Economics Working Papers 241, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  6. Oliver Hart & John Moore, 1988. "Property Rights and the Nature of the Firm," Working papers 495, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Sutton, John, 1986. "Non-cooperative Bargaining Theory: An Introduction," Review of Economic Studies, Wiley Blackwell, vol. 53(5), pages 709-24, October.
  8. Ray, D. & Vohra, R., 1993. "Equilibrium Binding Agreements," Papers 21, Boston University - Department of Economics.
  9. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
  10. Ray, Debraj & Vohra, Rajiv, 1999. "A Theory of Endogenous Coalition Structures," Games and Economic Behavior, Elsevier, vol. 26(2), pages 286-336, January.
  11. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  12. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-64, July.
  13. Bennett, Elaine, 1997. "Multilateral Bargaining Problems," Games and Economic Behavior, Elsevier, vol. 19(2), pages 151-179, May.
  14. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  15. 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.
  16. 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.
  17. 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.
  18. Krishna, Vijay & Serrano, Roberto, 1996. "Multilateral Bargaining," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 61-80, January.
  19. Martin J. Osborne & Ariel Rubinstein, 2005. "Bargaining and Markets," Levine's Bibliography 666156000000000515, UCLA Department of Economics.
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Cited by:

  1. Lindqvist, Tobias & Stennek, Johan, 2001. "The Insiders' Dilemma: An Experiment on Merger Formation," Research Papers in Economics 2001:8, Stockholm University, Department of Economics.
  2. 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.
  3. Tobias Lindqvist & Johan Stennek, 2005. "The Insiders’ Dilemma: An Experiment on Merger Formation," Experimental Economics, Springer, vol. 8(3), pages 267-284, September.

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