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On the Impossibility of Regret Minimization in Repeated Games

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  • Karl Schlag

    ()
    (University of Vienna)

  • Andriy Zapechelnyuk

    (Queen Mary, University of London)

Abstract

Regret minimizing strategies for repeated games have been receiving increasing attention in the literature. These are simple adaptive behavior rules that exhibit nice convergence properties. If all players follow regret minimizing strategies, their average joint play converges to the set of correlated equilibria or to the Hannan set (depending on the notion of regret in use), or even to Nash equilibrium on certain classes of games. In this note we raise the question of validity of the regret minimization objective. By example we show that regret minimization can lead to unrealistic behavior, since it fails to take into account the effect of one's actions on subsequent behavior of the opponents. An amended notion of regret that corrects this defect is not very useful either, since achieving a no-regret objective is not guaranteed in that case.

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Paper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 676.

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Date of creation: Dec 2010
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Handle: RePEc:qmw:qmwecw:wp676

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Keywords: Repeated games; Regret minimization; No-regret strategy;

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  1. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
  2. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  3. N. Littlestone & M. Warmuth, 2010. "The Weighted Majority Algorithm," Levine's Working Paper Archive 575, David K. Levine.
  4. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
  5. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
  6. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
  7. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  8. D. Foster & R. Vohra, 2010. "Asymptotic Calibration," Levine's Working Paper Archive 468, David K. Levine.
  9. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, September.
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