On the Impossibility of Regret Minimization in Repeated Games
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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- Sergiu Hart & Andreu Mas-Colell, 1997.
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Game Theory and Information
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- Sergiu Hart, 2013.
World Scientific Book Chapters,
in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287
World Scientific Publishing Co. Pte. Ltd..
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"A General Class of Adaptive Strategies,"
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- Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
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"A wide range no-regret theorem,"
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- 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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