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Better-Reply Strategies with Bounded Recall

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  • Andriy Zapechelnyuk

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Abstract

A decision maker (an agent) is engaged in a repeated interaction with Nature. The objective of the agent is to guarantee to himself the long-run average payoff as large as the best-reply payoff to Nature?s empirical distribution of play, no matter what Nature does. An agent 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: An agent 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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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp449.

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Length: 22 pages
Date of creation: Mar 2007
Date of revision:
Handle: RePEc:huj:dispap:dp449

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Keywords: Better-Reply Strategies; Regret; Bounded Recall; Fictitious Play; Approachability;

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  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, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  3. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
  4. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
  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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