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On Equilibrium Refinement in Supermodular Games

Author

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  • Oriol Carbonell-Nicolau

    (Rutgers University)

  • Richard McLean

    (Rutgers University)

Abstract

We show that supermodular games satisfying sequential better-reply security possess a pure strategy perfect equilibrium and a strategically stable set of pure strategies. We illustrate that, in continuous supermodular games, perfect equilibria may contain weakly dominated actions. Moreover, in discontinuous supermodular games, perfect equilibria may involve play of actions in the interior of the set of weakly dominated actions. We prove that when the set of undominated actions is a sublattice, supermodular games satisfying sequential better-reply security possess pure strategy perfect equilibria that can be obtained as limits of undominated actions.

Suggested Citation

  • Oriol Carbonell-Nicolau & Richard McLean, 2012. "On Equilibrium Refinement in Supermodular Games," Departmental Working Papers 201207, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:201207
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    References listed on IDEAS

    as
    1. Oriol Carbonell-Nicolau, 2011. "The Existence of Perfect Equilibrium in Discontinuous Games," Games, MDPI, vol. 2(3), pages 1-22, July.
    2. Carbonell-Nicolau, Oriol, 2011. "On strategic stability in discontinuous games," Economics Letters, Elsevier, vol. 113(2), pages 120-123.
    3. 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.
    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.
    5. Kultti, Klaus & Salonen, Hannu, 1997. "Undominated Equilibria in Games with Strategic Complementarities," Games and Economic Behavior, Elsevier, vol. 18(1), pages 98-115, January.
    6. Simon, Leo K & Stinchcombe, Maxwell B, 1995. "Equilibrium Refinement for Infinite Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1421-1443, November.
    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. Carbonell-Nicolau, Oriol, 2014. "On essential, (strictly) perfect equilibria," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 157-162.
    9. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    10. Al-Najjar, Nabil, 1995. "Strategically stable equilibria in games with infinitely many pure strategies," Mathematical Social Sciences, Elsevier, vol. 29(2), pages 151-164, April.
    11. 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.
    12. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    13. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    14. 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.
    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. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, December.
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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; trembling-hand perfect equilibrium; strategically stable set;
    All these keywords.

    JEL classification:

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

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