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Limit Behavior of No-regret Dynamics

Author

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  • Andriy Zapechelnyuk

    () (University of Bonn and Kyiv School of Economics)

Abstract

Consider a repeated game where all players follow no-regret strategies by reinforcing the actions that they regret not having played enough in the past. We show that a resulting no-regret dynamic approaches in the long run a best-response dynamic and leads to its invariant sets: rest points (Nash equilibria) or periodic orbits. The convergence results for best-response dynamics known in the literature immediately apply to no-regret dynamics. Thus, every no-regret dynamic leads to Nash equilibrium in zero-sum games, weighted potential and two-player ordinal potential games, supermodular games with diminishing returns, and some other special classes.

Suggested Citation

  • Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  • Handle: RePEc:kse:dpaper:21 Note: Under review in Journal of Economic Theory
    as

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    File URL: http://repec.kse.org.ua/pdf/KSE_dp21.pdf
    File Function: First version, October 2009
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Regret minimization; no-regret strategy; best-response dynamic; Nash equilibrium; Shapley polygon; curb set;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • 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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