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Characterizations of the Existence of Nash Equilibria with Non-convex Strategy Sets

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  • Rabia Nessah

    ()
    (IESEG School of Management (LEM-CNRS))

  • Kristiaan Kerstens

    ()
    (CNRS-LEM (UMR 8179), IESEG School of Management)

Abstract

A sufficient and necessary condition is presented for the existence of a Nash equilibrium in n-person noncooperative games in normal form where strategy sets are not necessarily convex. Under the convexity condition, we show that this new sufficient and necessary condition is a particular case of diagonal transfer quasiconcavity. The result is illustrated with an application to an economy with multilateral environmental externalities and to the existence of a Cournot equilibrium.

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Bibliographic Info

Paper provided by IESEG School of Management in its series Working Papers with number 2008-ECO-13.

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Length: 17 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:ies:wpaper:e200813

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Keywords: Noncooperative game; Nash equilibrium; convexity condition;

References

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  1. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  2. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  3. CHANDER, Parkash & TULKENS, Henry, 1995. "The Core of an Economy with Multilateral Environmental Externalities," CORE Discussion Papers 1995050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Baye, Michael R & Tian, Guoqiang & Zhou, Jianxin, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Wiley Blackwell, vol. 60(4), pages 935-48, October.
  5. Parkash Chander, 2007. "The gamma-core and coalition formation," International Journal of Game Theory, Springer, vol. 35(4), pages 539-556, April.
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  7. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
  8. Conley, John P. & Wilkie, Simon, 1996. "An Extension of the Nash Bargaining Solution to Nonconvex Problems," Games and Economic Behavior, Elsevier, vol. 13(1), pages 26-38, March.
  9. Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-48, October.
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  11. Wilson, Robert, 1997. "Nonlinear Pricing," OUP Catalogue, Oxford University Press, number 9780195115826.
  12. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part I: Generalities," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January.
  13. Scarf, Herbert E, 1981. "Production Sets with Indivisibilities-Part II: The Case of Two Activities," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March.
  14. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
  15. Xu, Yongsheng & Yoshihara, Naoki, 2006. "Alternative characterizations of three bargaining solutions for nonconvex problems," Games and Economic Behavior, Elsevier, vol. 57(1), pages 86-92, October.
  16. Peter Bogetoft, 1994. "Incentive Efficient Production Frontiers: An Agency Perspective on DEA," Management Science, INFORMS, vol. 40(8), pages 959-968, August.
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