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On equilibrium refinements in supermodular games

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  • Oriol Carbonell-Nicolau
  • Richard McLean

Abstract

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategy equilibria. We illustrate that in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games satisfying sequential better-reply security, perfect equilibria may involve play of actions in the interior of the set of weakly dominated actions. We show that supermodular games satisfying sequential better-reply security possess pure strategy perfect equilibria outside the interior of the set of weakly dominated action profiles. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Oriol Carbonell-Nicolau & Richard McLean, 2015. "On equilibrium refinements in supermodular games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 869-890, November.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:4:p:869-890
    DOI: 10.1007/s00182-014-0457-3
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    References listed on IDEAS

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    1. Carbonell-Nicolau, Oriol, 2011. "On strategic stability in discontinuous games," Economics Letters, Elsevier, vol. 113(2), pages 120-123.
    2. Carbonell-Nicolau, Oriol, 2014. "On essential, (strictly) perfect equilibria," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 157-162.
    3. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    4. Oriol Carbonell-Nicolau & Richard McLean, 2013. "Approximation results for discontinuous games with an application to equilibrium refinement," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 1-26, September.
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    7. Salonen, Hannu, 1996. "On the Existence of Undominated Nash Equilibria in Normal Form Games," Games and Economic Behavior, Elsevier, vol. 14(2), pages 208-219, June.
    8. 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.
    9. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    10. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, vol. 2(3), pages 1-22, July.
    11. Oriol Carbonell-Nicolau, 2011. "On Equilibrium Refinement For Discontinuous Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 269-280.
    12. Kultti, Klaus & Salonen, Hannu, 1997. "Undominated Equilibria in Games with Strategic Complementarities," Games and Economic Behavior, Elsevier, vol. 18(1), pages 98-115, January.
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    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. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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    Cited by:

    1. Takashi Kamihigashi & Kerim Keskin & Çağrı Sağlam, 2021. "Organizational refinements of Nash equilibrium," Theory and Decision, Springer, vol. 91(3), pages 289-312, October.
    2. Shinohara, Ryusuke, 2019. "Undominated coalition-proof Nash equilibria in quasi-supermodular games with monotonic externalities," Economics Letters, Elsevier, vol. 176(C), pages 86-89.
    3. Oriol Carbonell-Nicolau, 2021. "Perfect equilibria in games of incomplete information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1591-1648, June.

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    More about this item

    Keywords

    Supermodular game; Weakly dominated strategy; Perfect equilibrium; Strategically stable set; C72;
    All these keywords.

    JEL classification:

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

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