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Stochastic Uncoupled Dynamics and Nash Equilibrium

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Author Info
Sergiu Hart
Andreu Mas-Colell ()

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Abstract

In this paper we consider dynamic processes, in repeated games, that are subject to the natural informational restriction of uncoupledness. We study the almost sure convergence to Nash equilibria, and present a number of possibility and impossibility results. Basically, we show that if in addition to random moves some recall is introduced, then successful search procedures that are uncoupled can be devised. In particular, to get almost sure convergence to pure Nash equilibria when these exist, it su±ces to recall the last two periods of play.

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Publisher Info
Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 783.

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Date of creation: Oct 2004
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Handle: RePEc:upf:upfgen:783

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Web page: http://www.econ.upf.edu/

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Related research
Keywords: Uncoupled; Nash equilibrium; stochastic dynamics; bounded recall;

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Foster, Dean P. & Young, H. Peyton, 2003. "Learning, hypothesis testing, and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 45(1), pages 73-96, October. [Downloadable!] (restricted)
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  2. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash Convergence of Foster and Young's Regret Testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  3. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July. [Downloadable!] (restricted)
  4. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics. [Downloadable!]
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  5. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October. [Downloadable!] (restricted)
  6. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December. [Downloadable!]
  7. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. H. Peyton Young, 2008. "Learning by Trial and Error," Economics Series Working Papers 384, University of Oxford, Department of Economics. [Downloadable!]
    Other versions:
  2. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash Convergence of Foster and Young's Regret Testing," Economics Working Papers 788, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
    Other versions:
  3. George J. Mailath & : Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Second Version," PIER Working Paper Archive 08-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2008. [Downloadable!]
  4. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics. [Downloadable!]
  5. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Levine's Bibliography 843644000000000369, UCLA Department of Economics. [Downloadable!]
  6. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine. [Downloadable!]
  7. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Discussion Paper Series dp459, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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