No-regret Dynamics and Fictitious Play

Yannick Viossat (1) , Andriy Zapechelnyuk (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Economics and Finance, Queen Mary, University of London

Potential based no-regret dynamics are shown to be related to fictitious play. Roughly, these are epsilon-best reply dynamics where epsilon 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.

Mots clés: Regret minimization; no-regret strategy; fictitious play; best reply dynamics; Nash equilibrium; Hannan set; curb set

Domaines: Economies et finances; Systèmes dynamiques [math.DS]

Yannick Viossat, Andriy Zapechelnyuk. No-regret Dynamics and Fictitious Play. Journal of Economic Theory, 2013, 148 (2), pp.825-842. ⟨10.1016/j.jet.2012.07.003⟩. ⟨hal-00713871v2⟩