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Better-Reply Dynamics with Bounded Recall


  • Andriy Zapechelnyuk

    () (Kyiv School of Economics)


A decision maker is engaged in a repeated interaction with Nature. The objective of the decision maker is to guarantee to himself the average payoff as large as the best-reply payoff to Nature's empirical distribution of play, no matter what Nature does. The decision maker with perfect recall can achieve this objective by a simple better-reply strategy. In this paper we demonstrate that the relationship between perfect recall and bounded recall is not straightforward: The decision maker with bounded recall may fail to achieve this objective, no matter how long recall he has and no matter what better-reply strategy he employs.

Suggested Citation

  • Andriy Zapechelnyuk, 2008. "Better-Reply Dynamics with Bounded Recall," Discussion Papers 2, Kyiv School of Economics, revised Mar 2008.
  • Handle: RePEc:kse:dpaper:2 Note: Published in Mathematics of Operations Research, 33, 869-879 (2008)

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    References listed on IDEAS

    1. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    2. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
    3. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    4. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
    5. Ehud Lehrer & Eilon Solan, 2003. "No-Regret with Bounded Computational Capacity," Discussion Papers 1373, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    2. repec:eee:jetheo:v:169:y:2017:i:c:p:145-169 is not listed on IDEAS
    3. Schlag, Karl H. & Zapechelnyuk, Andriy, 2017. "Dynamic benchmark targeting," Journal of Economic Theory, Elsevier, vol. 169(C), pages 145-169.

    More about this item


    Better-reply dynamics; regret; bounded recall; fictitious play; approachability;

    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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