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Refinements of Nash equilibrium in potential games

Author

Listed:
  • Carbonell-Nicolau, Oriol

    () (Department of Economics, Rutgers University)

  • McLean, Richard P.

    () (Department of Economics, Rutgers University)

Abstract

We prove the existence of a pure-strategy trembling-hand perfect equilibrium in upper semicontinuous potential games, and we show that generic potential games possess pure-strategy strictly perfect and essential equilibria. We also establish a more powerful result: the set of maximizers of an upper semicontinuous potential contains a strategically stable set of pure-strategy Nash equilibria.

Suggested Citation

  • Carbonell-Nicolau, Oriol & McLean, Richard P., 2014. "Refinements of Nash equilibrium in potential games," Theoretical Economics, Econometric Society, vol. 9(3), September.
  • Handle: RePEc:the:publsh:1178
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    References listed on IDEAS

    as
    1. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, Open Access Journal, vol. 2(3), pages 1-22, July.
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    4. Carbonell-Nicolau, Oriol, 2011. "On strategic stability in discontinuous games," Economics Letters, Elsevier, vol. 113(2), pages 120-123.
    5. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    6. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
    7. 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.
    8. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March.
    9. Carbonell-Nicolau, Oriol, 2010. "Essential equilibria in normal-form games," Journal of Economic Theory, Elsevier, vol. 145(1), pages 421-431, January.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    11. Ui, Takashi, 2001. "Robust Equilibria of Potential Games," Econometrica, Econometric Society, vol. 69(5), pages 1373-1380, September.
    12. Atsushi Kajii & Stephen Morris, 1997. "The Robustness of Equilibria to Incomplete Information," Econometrica, Econometric Society, vol. 65(6), pages 1283-1310, November.
    13. Carbonell-Nicolau, Oriol, 2011. "Perfect and limit admissible perfect equilibria in discontinuous games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 531-540.
    14. Mclennan, A., 1989. "Selected Topics In The Theory Of Fixed Points," Papers 251, Minnesota - Center for Economic Research.
    15. Carbonell-Nicolau, Oriol, 2011. "On the existence of pure-strategy perfect equilibrium in discontinuous games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 23-48, January.
    16. DavidP. Myatt & Chris Wallace, 2009. "Evolution, Teamwork and Collective Action: Production Targets in the Private Provision of Public Goods," Economic Journal, Royal Economic Society, vol. 119(534), pages 61-90, January.
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    Cited by:

    1. Laurent Lamy & Philippe Jehiel, 2016. "On the benefits of set-asides," Post-Print hal-01688237, HAL.
    2. repec:ebl:ecbull:eb-17-00487 is not listed on IDEAS
    3. Vincent Boucher, 2017. "Selecting Equilibria using Best-Response Dynamics," Cahiers de recherche 1709, Centre de recherche sur les risques, les enjeux économiques, et les politiques publiques.
    4. Boucher, Vincent, 2016. "Conformism and self-selection in social networks," Journal of Public Economics, Elsevier, vol. 136(C), pages 30-44.

    More about this item

    Keywords

    Discontinuous game; potential game; trembling-hand perfect equilibrium; stable set; essential equilibrium;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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