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Better-Reply Dynamics with Bounded Recall

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  • Andriy Zapechelnyuk

    ()
    (Kyiv School of Economics)

Abstract

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.

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File URL: http://repec.kse.org.ua/pdf/KSE_dp2.pdf
File Function: Revised version, March 2008
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Bibliographic Info

Paper provided by Kyiv School of Economics in its series Discussion Papers with number 2.

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Date of creation: Jan 2008
Date of revision: Mar 2008
Handle: RePEc:kse:dpaper:2

Note: Published in Mathematics of Operations Research, 33, 869-879 (2008)
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Related research

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

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References

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  1. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
  2. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  3. 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.
  4. 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.
  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. Rene Saran & Roberto Serrano, 2010. "Regret matching with finite memory," Working Papers 2010-10, Instituto MadrileƱo de Estudios Avanzados (IMDEA) Ciencias Sociales.
  3. Saran Rene & Serrano Roberto, 2010. "Regret Matching with Finite Memory," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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