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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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 42 (2003)
Issue (Month): 1 (January)
Pages: 101-115

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Handle: RePEc:eee:gamebe:v:42:y:2003:i:1:p:101-115

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer, vol. 31(2), pages 253-268.
  2. 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.
  3. Fudenberg, Drew & Levine, David, 1999. "Conditional Universal Consistency," Scholarly Articles 3204826, Harvard University Department of Economics.
  4. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
  5. 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.
  6. Rustichini, Aldo, 1999. "Minimizing Regret: The General Case," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 224-243, October.
  7. 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.
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Citations

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Cited by:
  1. Karl Schlag & Andriy Zapechelnyuk, 2009. "Decision making in uncertain and changing environments," Economics Working Papers 1160, Department of Economics and Business, Universitat Pompeu Fabra.
  2. 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.
  3. 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.
  4. Yuichi Noguchi, 2009. "Note on universal conditional consistency," International Journal of Game Theory, Springer, vol. 38(2), pages 193-207, June.
  5. 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.
  6. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics.
  7. Hu, Tai Wei & Shmaya, Eran, 2013. "Expressible inspections," Theoretical Economics, Econometric Society, vol. 8(2), May.
  8. 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.
  9. 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.
  10. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
  11. repec:hal:wpaper:hal-00713871 is not listed on IDEAS
  12. Viossat, Yannick & Zapechelnyuk, Andriy, 2013. "No-regret dynamics and fictitious play," Journal of Economic Theory, Elsevier, vol. 148(2), pages 825-842.

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