Limit Behavior of No-regret Dynamics

Andriy Zapechelnyuk

No 21, Discussion Papers from 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.

Keywords: Regret minimization; no-regret strategy; best-response dynamic; Nash equilibrium; Shapley polygon; curb set (search for similar items in EconPapers)
JEL-codes: C44 D81 D83 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-evo and nep-gth
Date: 2009-10
Note: Under review in Journal of Economic Theory
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http://www.kse.org.ua/RePEc/pdf/KSE_dp21.pdf First version, October 2009 (application/pdf)

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