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No-regret dynamics and fictitious play

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  • Viossat, Yannick
  • Zapechelnyuk, Andriy

Abstract

Potential based no-regret dynamics are shown to be related to fictitious play. Roughly, these are ε-best reply dynamics where ε is the maximal regret, which vanishes with time. This allows for alternative and sometimes much shorter proofs of known results on convergence of no-regret dynamics to the set of Nash equilibria.

Suggested Citation

  • Viossat, Yannick & Zapechelnyuk, Andriy, 2013. "No-regret dynamics and fictitious play," Journal of Economic Theory, Elsevier, vol. 148(2), pages 825-842.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:825-842
    DOI: 10.1016/j.jet.2012.07.003
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    Cited by:

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    3. Christoph Graf & Viktor Zobernig & Johannes Schmidt & Claude Klöckl, 2024. "Computational Performance of Deep Reinforcement Learning to Find Nash Equilibria," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 529-576, February.
    4. Panayotis Mertikopoulos & William H. Sandholm, 2016. "Learning in Games via Reinforcement and Regularization," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1297-1324, November.
    5. Leslie, David S. & Perkins, Steven & Xu, Zibo, 2020. "Best-response dynamics in zero-sum stochastic games," Journal of Economic Theory, Elsevier, vol. 189(C).

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    More about this item

    Keywords

    Regret minimization; No-regret strategy; Fictitious play; Best-reply dynamics; Nash equilibrium; Hannan set; Curb set;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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