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Coalitional Bargaining Equilibria

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  • John Duggan

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    (W. Allen Wallis Institute of Political Economy, 107 Harkness Hall, University of Rochester, Rochester, NY 14627-0158)

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    Abstract

    This paper takes up the foundational issue of existence of stationary subgame perfect equi- libria in a general class of coalitional bargaining games that includes many known bargaining models and models of coalition formation. General sufficient conditions for existence of equilib- ria are currently lacking in many interesting environments: bargaining models with non-concave stage utility functions, models with a Pareto optimal status quo alternative and heterogeneous discount factors, and models of coalition formation in public good economies with consumption lower bounds. This paper establishes existence of stationary equilibrium under compactness and continuity conditions, without the structure of convexity or comprehensiveness used in the extant literature. The proof requires a precise selection of voting equilibria following different proposals. The result is applied to obtain equilibria in models of bargaining over taxes, coalition formation in NTU environments, and collective dynamic programming problems.

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    Bibliographic Info

    Paper provided by University of Rochester - Wallis Institute of Political Economy in its series Wallis Working Papers with number WP62.

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    Length: 33 pages
    Date of creation: May 2011
    Date of revision:
    Handle: RePEc:roc:wallis:wp62

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    Postal: University of Rochester, Wallis Institute, Harkness 109B Rochester, New York 14627 U.S.A.

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    1. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
    2. Okada, Akira, 1996. "A Noncooperative Coalitional Bargaining Game with Random Proposers," Games and Economic Behavior, Elsevier, vol. 16(1), pages 97-108, September.
    3. Konstantin Sonin & Georgy Egorov & Daron Acemoglu, 2008. "Dynamics and Stability of Constitutions, Coalitions and Clubs," 2008 Meeting Papers 314, Society for Economic Dynamics.
    4. Roberto Serrano, 2007. "Nash program," Working Papers 2007-05, Instituto MadrileƱo de Estudios Avanzados (IMDEA) Ciencias Sociales.
    5. Borgers, Tilman, 1989. "Perfect equilibrium histories of finite and infinite horizon games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 218-227, February.
    6. Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
    7. Borgers, Tilman, 1991. "Upper hemicontinuity of the correspondence of subgame-perfect equilibrium outcomes," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 89-106.
    8. Ray, Debraj, 2007. "A Game-Theoretic Perspective on Coalition Formation," OUP Catalogue, Oxford University Press, number 9780199207954.
    9. Eraslan, Hulya & Merlo, Antonio, 2002. "Majority Rule in a Stochastic Model of Bargaining," Journal of Economic Theory, Elsevier, vol. 103(1), pages 31-48, March.
    10. Siddhartha Bandyopadhyay & Kalyan Chatterjee, 2006. "Coalition Theory and its Applications: A Survey," Economic Journal, Royal Economic Society, vol. 116(509), pages F136-F155, 02.
    11. Konishi, Hideo & Ray, Debraj, 2003. "Coalition formation as a dynamic process," Journal of Economic Theory, Elsevier, vol. 110(1), pages 1-41, May.
    12. Tasos Kalandrakis, 2010. "Minimum winning coalitions and endogenous status quo," International Journal of Game Theory, Springer, vol. 39(4), pages 617-643, October.
    13. Kalandrakis, Anastassios, 2004. "A three-player dynamic majoritarian bargaining game," Journal of Economic Theory, Elsevier, vol. 116(2), pages 294-322, June.
    14. Banks, Jeffrey S. & Duggan, John, 2006. "A General Bargaining Model of Legislative Policy-making," International Quarterly Journal of Political Science, now publishers, vol. 1(1), pages 49-85, January.
    15. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-44, May.
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    Cited by:
    1. Herings P. Jean-Jacques & Britz Volker & Predtetchinski Arkadi, 2012. "On the Convergence to Nash Bargaining Solution for Endogenous Bargaining Protocols," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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