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A wide range no-regret theorem

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  • Lehrer, Ehud

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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  • Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
    • Handle: RePEc:eee:gamebe:v:42:y:2003:i:1:p:101-115
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    References listed on IDEAS

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    1. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 253-268.
    2. 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.
    3. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
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    5. Rustichini, Aldo, 1999. "Minimizing Regret: The General Case," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 224-243, October.
    6. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    7. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    8. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    9. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(1), pages 57-89.
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    Cited by:

    1. Viossat, Yannick & Zapechelnyuk, Andriy, 2013. "No-regret dynamics and fictitious play," Journal of Economic Theory, Elsevier, vol. 148(2), pages 825-842.
    2. Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    3. Yuichi Noguchi, 2009. "Note on universal conditional consistency," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 193-207, June.
    4. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
    5. , & ,, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
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    7. Arifovic, Jasmina & Boitnott, Joshua F. & Duffy, John, 2019. "Learning correlated equilibria: An evolutionary approach," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 171-190.
    8. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
    9. 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.
    10. Ludovico Crippa & Yonatan Gur & Bar Light, 2022. "Equilibria in Repeated Games under No-Regret with Dynamic Benchmarks," Papers 2212.03152, arXiv.org, revised Jul 2023.
    11. Shira Daskal & Adar Ben-Eliyahu & Gal Levy & Yakov Ben-Haim & Ronnen Avny, 2022. "Earthquake Vulnerability Reduction by Building a Robust Social-Emotional Preparedness Program," Sustainability, MDPI, vol. 14(10), pages 1-22, May.
    12. Karl Schlag & Andriy Zapechelnyuk, 2009. "Decision Making in Uncertain and Changing Environments," Discussion Papers 19, Kyiv School of Economics.
    13. Schlag, Karl H. & Zapechelnyuk, Andriy, 2017. "Dynamic benchmark targeting," Journal of Economic Theory, Elsevier, vol. 169(C), pages 145-169.
    14. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, vol. 59(1), pages 187-208, April.
    15. Mannor, Shie & Shimkin, Nahum, 2008. "Regret minimization in repeated matrix games with variable stage duration," Games and Economic Behavior, Elsevier, vol. 63(1), pages 227-258, May.
    16. Schlag, Karl & Zapechelnyuk, Andriy, 2012. "On the impossibility of achieving no regrets in repeated games," Journal of Economic Behavior & Organization, Elsevier, vol. 81(1), pages 153-158.
    17. Karl Schlag & Andriy Zapechelnyuk, 2010. "On the Impossibility of Regret Minimization in Repeated Games," Working Papers 676, Queen Mary University of London, School of Economics and Finance.

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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