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On the impossibility of achieving no regrets in repeated games

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Author Info

  • Schlag, Karl
  • Zapechelnyuk, Andriy

Abstract

Regret-minimizing strategies for repeated games have been receiving increasing attention in the literature. These are simple adaptive behavior rules that lead to no regrets and, if followed by all players, exhibit nice convergence properties: the average play converges to correlated equilibrium, or even to Nash equilibrium in certain classes of games. However, the no-regret property relies on a strong assumption that each player treats her opponents as unresponsive and fully ignores the opponents’ possible reactions to her actions. We show that if at least one player is slightly responsive, it is impossible to achieve no regrets, and convergence results for regret minimization with responsive opponents are unknown.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 81 (2012)
Issue (Month): 1 ()
Pages: 153-158

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Handle: RePEc:eee:jeborg:v:81:y:2012:i:1:p:153-158

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Web page: http://www.elsevier.com/locate/jebo

Related research

Keywords: C73; D81; D83; Adaptive strategies; Regret minimization; Regret matching;

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  1. 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.
  2. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
  3. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
  4. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  5. 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.
  6. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  7. Fudenberg, Drew & Levine, David K., 1995. "Consistency and cautious fictitious play," Journal of Economic Dynamics and Control, Elsevier, vol. 19(5-7), pages 1065-1089.
  8. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
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