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Stochastic uncoupled dynamics and Nash equilibrium

  • Hart, Sergiu
  • Mas-Colell, Andreu

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

Volume (Year): 57 (2006)
Issue (Month): 2 (November)
Pages: 286-303

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Handle: RePEc:eee:gamebe:v:57:y:2006:i:2:p:286-303
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
  2. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
  3. 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.
  4. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  5. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  6. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
  7. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
  8. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
  9. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, March.
  10. 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.
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