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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
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    References listed on IDEAS

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    1. Mark Voorneveld & Peter Borm & Freek Van Megen & Stef Tijs & Giovanni Facchini, 1999. "Congestion Games And Potentials Reconsidered," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 283-299.
    2. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    3. 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.
    4. 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.
    5. Shin, Sungwhee & Suh, Sang-Chul, 1996. "A mechanism implementing the stable rule in marriage problems," Economics Letters, Elsevier, vol. 51(2), pages 185-189, May.
    6. 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.
    7. Mark Voorneveld & Sofia Grahn, 2002. "Cost allocation in shortest path games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 323-340, November.
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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.
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    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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