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Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement

Author

Listed:
  • Oriol Carbonell-Nicolau

    (Rutgers University)

  • Richard McLean

    (Rutgers University)

Abstract

We provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed. We then prove existence results for a new "finitistic" infinite-game generalization of Selten's [24] notion of perfection, and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification.

Suggested Citation

  • Oriol Carbonell-Nicolau & Richard McLean, 2012. "Approximation Results for Discontinuous Games with an Application to Equilibrium Refinement," Departmental Working Papers 201206, Rutgers University, Department of Economics.
    • Handle: RePEc:rut:rutres:201206
    as

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    References listed on IDEAS

    as
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    Cited by:

    1. M. Ali Khan & Metin Uyanik, 2021. "The Yannelis–Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 799-840, April.
    2. Carbonell-Nicolau, Oriol, 2014. "On essential, (strictly) perfect equilibria," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 157-162.
    3. 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.
    4. 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.
    5. Alejandro Saporiti, 2014. "Power sharing and electoral equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 705-729, April.
    6. He, Wei & Yannelis, Nicholas C., 2016. "Existence of equilibria in discontinuous Bayesian games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 181-194.
    7. Oriol Carbonell-Nicolau, 2015. "Further results on essential Nash equilibria in normal-form games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 277-300, June.
    8. 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.
    9. 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.

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    More about this item

    Keywords

    discontinuous game; Nash equilibrium correspondence; better-reply security; equilibrium refinement; limit-of-finite perfect equilibrium;
    All these keywords.

    JEL classification:

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

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