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Sampled fictitious play is Hannan consistent

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  • Li, Zifan
  • Tewari, Ambuj

Abstract

Fictitious play is a simple and widely studied adaptive heuristic for playing repeated games. It is well known that fictitious play fails to be Hannan consistent. Several variants of fictitious play including regret matching, generalized regret matching and smooth fictitious play, are known to be Hannan consistent. In this note, we consider sampled fictitious play: at each round, the player samples past times and plays the best response to previous moves of other players at the sampled time points. We show that sampled fictitious play, using Bernoulli sampling, is Hannan consistent. Unlike several existing Hannan consistency proofs that rely on concentration of measure results, ours instead uses anti-concentration results from Littlewood–Offord theory.

Suggested Citation

  • Li, Zifan & Tewari, Ambuj, 2018. "Sampled fictitious play is Hannan consistent," Games and Economic Behavior, Elsevier, vol. 109(C), pages 401-412.
    • Handle: RePEc:eee:gamebe:v:109:y:2018:i:c:p:401-412
    DOI: 10.1016/j.geb.2018.01.005
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    More about this item

    Keywords

    Adaptive heuristics; Learning; Repeated games; Hannan consistency; Fictitious play;
    All these keywords.

    JEL classification:

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

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