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A General Class of Adaptive Strategies

  • Sergiu Hart

    (The Hebrew University of Jerusalem, Israel)

  • Andreu Mas-Colell

    (Universitat Pompeu Fabra, Barcelona, Spain)

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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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.
Contact details of provider: Web page: http://econwpa.repec.org

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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. D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
  3. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
  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. D. Blackwell, 2010. "Controlled Random Walks," Levine's Working Paper Archive 465, David K. Levine.
  6. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  7. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
  8. D. Foster & R. Vohra, 2010. "Calibrated Learning and Correlated Equilibrium," Levine's Working Paper Archive 568, David K. Levine.
  9. 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.
  10. 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.
  11. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  12. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
  13. Dov Monderer & Dov Samet & Aner Sela, 1994. "Belief Affirming in Learning Processes," Game Theory and Information 9408002, EconWPA, revised 11 Aug 1994.
  14. Fudenberg, Drew & Levine, David, 1999. "Conditional Universal Consistency," Scholarly Articles 3204826, Harvard University Department of Economics.
  15. 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.
  16. N. Littlestone & M. Warmuth, 2010. "The Weighted Majority Algorithm," Levine's Working Paper Archive 575, David K. Levine.
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