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A General Class of Adaptative Strategies

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Author Info
Sergiu Hart
Andreu Mas-Colell ()

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Abstract

We exhibit and characterize an entire class of simple adaptive strategies, in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the other players; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [1995]) and regret-matching (Hart and Mas-Colell [1998]) are particular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in the long-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a] approachability strategy for games with vector payoffs.

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Publisher Info
Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 373.

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Date of creation: Mar 1999
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Handle: RePEc:upf:upfgen:373

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Web page: http://www.econ.upf.edu/

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Related research
Keywords: Adaptive strategies; approachability; correlated equilibrium; fictitious play; regret;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D7 - Microeconomics - - Analysis of Collective Decision-Making
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October. [Downloadable!] (restricted)
  2. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
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  3. 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. [Downloadable!] (restricted)
  4. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
  5. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
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  7. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April. [Downloadable!] (restricted)
  8. Nimrod Megiddo, 1979. "On Repeated Games with Incomplete Information Played by Non-Bayesian Players," Discussion Papers 373, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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