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Sampling best response dynamics and deterministic equilibrium selection

Author

Listed:
  • Oyama Daisuke

    (Faculty of economics - UTokyo - The University of Tokyo)

  • William H. Sandholm

    (University of Wisconsin-Madison)

  • Olivier Tercieux

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

We consider a model of evolution in games in which a revising agent observes the actions of a random number of randomly sampled opponents and then chooses a best response to the distribution of actions in the sample. We provide a condition on the distribution of sample sizes under which an iterated p-dominant equilibrium is almost globally asymptotically stable under these dynamics. We show under an additional condition on the sample size distribution that in supermodular games, an almost globally asymptotically stable state must be an iterated p-dominant equilibrium. Since our selection results are for deterministic dynamics, any selected equilibrium is reached quickly; the long waiting times associated with equilibrium selection in stochastic stability models are absent.

Suggested Citation

  • Oyama Daisuke & William H. Sandholm & Olivier Tercieux, 2015. "Sampling best response dynamics and deterministic equilibrium selection," PSE-Ecole d'économie de Paris (Postprint) halshs-01157537, HAL.
  • Handle: RePEc:hal:pseptp:halshs-01157537
    DOI: 10.3982/TE1405
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01157537
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    More about this item

    Keywords

    equilibrium selection; Evolutionary game dynamics; almost global convergence; iterated p-dominance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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