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On the Existence of Strong Nash Equilibria

Author

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  • 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
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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
    File Function: Revised version, 2009
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    References listed on IDEAS

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    4. Naoki Yoshihara, 1999. "Natural and double implementation of public ownership solutions in differentiable production economies," Review of Economic Design, Springer;Society for Economic Design, vol. 4(2), pages 127-151.
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    7. Yi, Sang-Seung, 1999. "On the Coalition-Proofness of the Pareto Frontier of the Set of Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(2), pages 353-364, January.
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    Cited by:

    1. Zhe Yang & Haiqun Zhang, 2019. "NTU core, TU core and strong equilibria of coalitional population games with infinitely many pure strategies," Theory and Decision, Springer, vol. 87(2), pages 155-170, September.
    2. Eleonora Braggion & Nicola Gatti & Roberto Lucchetti & Tuomas Sandholm & Bernhard von Stengel, 2020. "Strong Nash equilibria and mixed strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 699-710, September.
    3. Yamamura, Hirofumi, 2016. "Coalitional stability in the location problem with single-dipped preferences: An application of the minimax theorem," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 48-57.

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    Keywords

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