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Conditional Universal Consistency

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Author Info

  • Drew Fudenberg
  • David K. Levine

Abstract

Players choose an action before learning an outcome chosen according to an unknown and history-dependent stochastic rule. Procedures that categorize outcomes, and use a randomized variation on fictitious play within each category are studied. These procedures are “conditionally consistent:†they yield almost as high a time-average payoff as if the player knew the conditional distributions of actions given categories. Moreover, given any alternative procedure, there is a conditionally consistent procedure whose performance is no more than epsilon worse regardless of the discount factor. We also discuss cycles, and argue that the time-average of play should resemble a correlated equilibrium.

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Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 471.

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Date of creation: 13 Aug 1997
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Handle: RePEc:cla:levarc:471

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Web page: http://www.dklevine.com/

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References

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  1. Sanchirico, Chris William, 1996. "A Probabilistic Model of Learning in Games," Econometrica, Econometric Society, vol. 64(6), pages 1375-93, November.
  2. Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. 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.
  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.
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  7. P. Auer & N. Cesa-Bianchi & Y. Freund & R. Schapire, 2010. "Gambling in a rigged casino: The adversarial multi-armed bandit problem," Levine's Working Paper Archive 462, David K. Levine.
  8. Drew Fudenberg & David K. Levine, 1996. "An Easier Way to Calibrate," Levine's Working Paper Archive 2059, David K. Levine.
  9. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  10. N. Megiddo, 2010. "On Repeated Games with Incomplete Information Played with Non-Bayesian Players," Levine's Working Paper Archive 480, David K. Levine.
  11. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  12. Aoyagi, Masaki, 1996. "Evolution of Beliefs and the Nash Equilibrium of Normal Form Games," Journal of Economic Theory, Elsevier, vol. 70(2), pages 444-469, August.
  13. M. Aoyagi, 2010. "Evolution of Beliefs and the Nash Equilibrium of a Normal Form Game," Levine's Working Paper Archive 562, David K. Levine.
  14. 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.
  15. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
  16. T.H. Chung, 2010. "Approximate Methods for Sequential Decision Making Using Expert Advice," Levine's Working Paper Archive 564, David K. Levine.
  17. Y. Freund & R. Schapire, 2010. "A Decision Theoretic Generalization of On-Line Learning and an Application to Boosting," Levine's Working Paper Archive 570, David K. Levine.
  18. M. Feder & N. Mehrav & M. Gutman, 2010. "Universal Prediction of Individual Sequences," Levine's Working Paper Archive 567, David K. Levine.
  19. Sonsino, Doron, 1997. "Learning to Learn, Pattern Recognition, and Nash Equilibrium," Games and Economic Behavior, Elsevier, vol. 18(2), pages 286-331, February.
  20. 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.
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