On the Impossibility of Regret Minimization in Repeated Games
AbstractRegret 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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Bibliographic InfoPaper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 676.
Date of creation: Dec 2010
Date of revision:
Repeated games; Regret minimization; No-regret strategy;
Find related papers by JEL classification:
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-01-16 (All new papers)
- NEP-GTH-2011-01-16 (Game Theory)
- NEP-HPE-2011-01-16 (History & Philosophy of Economics)
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