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Regret-based continuous-time dynamics

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  • Hart, Sergiu
  • Mas-Colell, Andreu

Abstract

Regret-based dynamics have been introduced and studied in the context of discrete-time repeated play. Here we carry out the corresponding analysis in continuous time. We observe that, in contrast to (smooth) fictitious play or to evolutionary models, the appropriate state space for this analysis is the space of distributions on the product of the players' pure action spaces (rather than the product of their mixed action spaces). We obtain relatively simple proofs for some results known in the discrete case (related to "no-regret" and correlated equilibria), and also a new result on two-person potential games (for this result we also provide a discrete-time proof).

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 45 (2003)
Issue (Month): 2 (November)
Pages: 375-394

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Handle: RePEc:eee:gamebe:v:45:y:2003:i:2:p:375-394

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. 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.
  2. Sandholm,W.H., 2002. "Potential dynamics and stable games," Working papers 21, Wisconsin Madison - Social Systems.
  3. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November.
  4. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, 05.
  5. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
  6. Sergiu Hart & Andreu Mas-Colell, 1999. "A General Class of Adaptive Strategies," Game Theory and Information 9904001, EconWPA, revised 23 Mar 2000.
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