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  • Karl H. Schlag

Abstract

We select among rules for learning which of two actions in a stationary decision problem achieves a higher expected payo¤when payoffs realized by both actions are known in previous instances. Only a bounded set containing all possible payoffs is known. Rules are evaluated using maximum risk with maximin utility, minimax regret, competitive ratio and selection procedures being special cases. A randomized variant of fictitious play attains minimax risk for all risk functions with ex-ante expected payoffs increasing in the number of observations. Fictitious play itself has neither of these two properties. Tight bounds on maximal regret and probability of selecting the best action are included.

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Bibliographic Info

Paper provided by European University Institute in its series Economics Working Papers with number ECO2007/01.

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Date of creation: 2007
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Handle: RePEc:eui:euiwps:eco2007/01

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Keywords: fictitious play; nonparametric; finite sample; matched pairs; foregone payoffs; minimax risk; ex-ante improving; selection procedure;

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  1. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  2. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
  3. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  4. Karl Schlag, 2006. "ELEVEN - Tests needed for a Recommendation," Economics Working Papers ECO2006/2, European University Institute.
  5. Jörg Stoye, 2011. "Statistical decisions under ambiguity," Theory and Decision, Springer, vol. 70(2), pages 129-148, February.
  6. Tilman Borgers & Antonio Morales & Rajiv Sarin, 2010. "Expedient and Monotone Learning Rules," Levine's Working Paper Archive 625018000000000099, David K. Levine.
  7. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
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