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On the Existence of Strong Nash Equilibria

Author

Listed:
  • Rabia Nessah

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

  • Guoqiang Tian

    (Texas A&M University, USA)

Abstract

This paper investigates the existence of strong Nashequilibria (SNE) in continuous and convex games. We show that the concavity and an additional condition on payoff functions, together with the compactness of strategy space, permit the existence of strong Nash equilibria. These conditions are satisfied in many economic games and are quite simple to check. We also characterize the existence of SNE by providing a necessary and sufficient condition. Moreover, we suggest a procedure that can be used to efficiently compute strong Nash equilibrium. The result is illustrated with an application to an economy with multilateral environmental externalities and to the simple oligopoly static model.

Suggested Citation

  • Rabia Nessah & Guoqiang Tian, 2009. "On the Existence of Strong Nash Equilibria," Working Papers 2009-ECO-06, IESEG School of Management.
  • Handle: RePEc:ies:wpaper:e200906
    as

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    File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=44045475_2009-ECO-06_Nessah_Tian.pdf
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    File URL: http://my.ieseg.fr/bienvenue/DownloadDoc.asp?Fich=230987888_2010-ECO-12_Nessah_Tian.pdf
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    References listed on IDEAS

    as
    1. Slikker, Marco & van den Nouweland, Anne, 2001. "A One-Stage Model of Link Formation and Payoff Division," Games and Economic Behavior, Elsevier, vol. 34(1), pages 153-175, January.
    2. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Non cooperative game; strong Nash equilibrium; weak Pareto-efficiency;

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