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A General Class of Adaptive Strategies

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  • Hart, Sergiu
  • Mas-Colell, Andreu

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 98 (2001)
Issue (Month): 1 (May)
Pages: 26-54

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Handle: RePEc:eee:jetheo:v:98:y:2001:i:1:p:26-54

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
  2. Monderer, Dov & Samet, Dov & Sela, Aner, 1997. "Belief Affirming in Learning Processes," Journal of Economic Theory, Elsevier, vol. 73(2), pages 438-452, April.
  3. Fudenberg, Drew & Levine, David, 1995. "Consistency and Cautious Fictitious Play," Scholarly Articles 3198694, Harvard University Department of Economics.
  4. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  5. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
  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. D. Blackwell, 2010. "Controlled Random Walks," Levine's Working Paper Archive 465, David K. Levine.
  8. Fudenberg, Drew & Levine, David, 1999. "Conditional Universal Consistency," Scholarly Articles 3204826, Harvard University Department of Economics.
  9. J. Robinson, 1969. "An Iterative Method of Solving a Game," Levine's Working Paper Archive 422, David K. Levine.
  10. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  11. 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.
  12. D. Foster & R. Vohra, 2010. "Regret in the On-line Decision Problem," Levine's Working Paper Archive 569, David K. Levine.
  13. 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.
  14. 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.
  15. N. Littlestone & M. Warmuth, 2010. "The Weighted Majority Algorithm," Levine's Working Paper Archive 575, David K. Levine.
  16. D. Foster & R. Vohra, 2010. "Calibrated Learning and Correlated Equilibrium," Levine's Working Paper Archive 568, David K. Levine.
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