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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)

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

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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Web page: http://128.118.178.162

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Keywords: No-regret; Approachability; large spaces;

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References

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  1. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  2. Ehud Lehrer, 2003. "Approachability in infinite dimensional spaces," International Journal of Game Theory, Springer, vol. 31(2), pages 253-268.
  3. Rustichini, A., 1998. "Minimizing Regret: The General Case," Discussion Paper 1998-41, Tilburg University, Center for Economic Research.
  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.
  5. 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.
  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.
  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.
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Citations

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