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A General Class of Adaptive Strategies

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Author Info

  • Sergiu Hart

    (The Hebrew University of Jerusalem, Israel)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Barcelona, Spain)

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 [2000]) are particular cases. The motivation and application of the current paper come from the study of procedures whose empirical distribution of play is, in the long-run, (almost) a correlated equilibrium. For the analysis we first develop a generalization of Blackwell's [1956a] approachability strategy for games with vector payoffs.

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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9904001.

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Date of creation: 12 Apr 1999
Date of revision: 23 Mar 2000
Handle: RePEc:wpa:wuwpga:9904001

Note: Type of Document - Scientific Word v.2.5. First version: March 1999. Revised: December 1999.
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Web page: http://128.118.178.162

Related research

Keywords: adaptive strategies; approachability; correlated equilibrium; fictitious play; regret;

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References

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  1. Drew Fudenberg & David K. Levine, 1996. "Consistency and Cautious Fictitious Play," Levine's Working Paper Archive 470, David K. Levine.
  2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  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.
  4. D. Foster & R. Vohra, 2010. "Calibrated Learning and Correlated Equilibrium," Levine's Working Paper Archive 568, David K. Levine.
  5. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  6. 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.
  7. N. Littlestone & M. Warmuth, 2010. "The Weighted Majority Algorithm," Levine's Working Paper Archive 575, David K. Levine.
  8. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
  9. Fudenberg, Drew & Levine, David, 1999. "Conditional Universal Consistency," Scholarly Articles 3204826, Harvard University Department of Economics.
  10. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
  11. D. Blackwell, 2010. "Controlled Random Walks," Levine's Working Paper Archive 465, David K. Levine.
  12. Dov Monderer & Dov Samet & Aner Sela, 1994. "Belief Affirming in Learning Processes," Game Theory and Information 9408002, EconWPA, revised 11 Aug 1994.
  13. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
  14. 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.
  15. D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
  16. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
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