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A Wide Range No-Regret Theorem

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Author Info
Ehud Lehrer (Tel Aviv U.)
Dinah Rosenberg (U. Paris Nord)

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Abstract

In a sequential decision problem at any stage a decision maker, based on the history, takes a decision and receives a payoff which depends also on the realized state of nature. A strategy, f, is said to be as good as an alternative strategy g at a sequence of states, if in the long run f does, on average, at least as well as g does. It is shown that for any distribution, P, over the alternative strategies there is a strategy f which is, at any sequence of states, as good as P-almost any alternative g.

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Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 0312004.

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Date of creation: 11 Dec 2003
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Handle: RePEc:wpa:wuwpga:0312004

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Related research
Keywords: No-regret; Approachability; large spaces;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Drew Fudenberg & David K. Levine, 1997. "Conditional Universal Consistency," Levine's Working Paper Archive 471, David K. Levine. [Downloadable!]
    Other versions:
  2. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer, vol. 31(2), pages 253-268. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. 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. [Downloadable!]
    Other versions:
  5. Rustichini, Aldo, 1999. "Minimizing Regret: The General Case," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 224-243, October. [Downloadable!] (restricted)
  6. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer, vol. 18(1), pages 57-89.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Yuichi Noguchi, 2009. "Note on universal conditional consistency," International Journal of Game Theory, Springer, vol. 38(2), pages 193-207, June. [Downloadable!] (restricted)
  2. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics. [Downloadable!]
  3. Karl H. Schlag & Andriy Zapechelnyuk, 2009. "Decision Making in Uncertain and Changing Environments," Levine's Working Paper Archive 814577000000000259, David K. Levine. [Downloadable!]
    Other versions:
  4. Ehud Lehrer & Eilon Solan, 2003. "No-Regret with Bounded Computational Capacity," Discussion Papers 1373, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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