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Stochastic uncoupled dynamics and Nash equilibrium

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  • Hart, Sergiu
  • Mas-Colell, Andreu

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 suffices to recall the last two periods of play.

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Bibliographic Info

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

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

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  1. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, Elsevier, vol. 45(2), pages 375-394, November.
  2. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive, The Johns Hopkins University,Department of Economics 474, The Johns Hopkins University,Department of Economics.
  3. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
  4. S. Hart & A. Mas-Collel, 2010. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Levine's Working Paper Archive 572, David K. Levine.
  5. 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.
  6. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, American Economic Association, vol. 93(5), pages 1830-1836, December.
  7. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(1), pages 5-39, March.
  8. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199269181, October.
  9. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, Elsevier, vol. 21(1-2), pages 40-55, October.
  10. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 5(3), pages 368-386, July.
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Cited by:
  1. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, Elsevier, vol. 71(1), pages 174-192, January.
  2. Yakov Babichenko, 2014. "How long to Pareto efficiency?," International Journal of Game Theory, Springer, Springer, vol. 43(1), pages 13-24, February.
  3. Pradelski, Bary S.R. & Young, H. Peyton, 2012. "Learning efficient Nash equilibria in distributed systems," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(2), pages 882-897.
  4. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp459, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. Itai Arieli & H Peyton Young, 2011. "Stochastic Learning Dynamics and Speed of Convergence in Population Games," Economics Series Working Papers 570, University of Oxford, Department of Economics.
  6. H Peyton Young & H.H. Nax & M.N. Burton-Chellew & S.A. West, 2013. "Learning in a Black Box," Economics Series Working Papers 653, University of Oxford, Department of Economics.
  7. Heinrich H. Nax & Maxwell N. Burton-Chellew & Stuart A. West & H. Peyton Young, 2013. "Learning in a Black Box," PSE Working Papers hal-00817201, HAL.
  8. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, Elsevier, vol. 65(2), pages 626-643, March.
  9. Hart, Sergiu & Mansour, Yishay, 2010. "How long to equilibrium? The communication complexity of uncoupled equilibrium procedures," Games and Economic Behavior, Elsevier, Elsevier, vol. 69(1), pages 107-126, May.
  10. 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.
  11. 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.
  12. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
  13. H Peyton Young & Jason R. Marden and Lucy Y. Pao, 2011. "Achieving Pareto Optimality Through Distributed Learning," Economics Series Working Papers 557, University of Oxford, Department of Economics.
  14. Vasin, A., 2010. "Evolutionary Game Theory and Economics. Part 2. Stability of Equilibria. Special Features of Human Behavior Evolution," Journal of the New Economic Association, New Economic Association, New Economic Association, issue 5, pages 10-27.
  15. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  16. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Levine's Bibliography 843644000000000369, UCLA Department of Economics.
  17. Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp600, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  18. Arieli, Itai & Babichenko, Yakov, 2012. "Average testing and Pareto efficiency," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(6), pages 2376-2398.
  19. Paul Goldberg & Rahul Savani & Troels Sørensen & Carmine Ventre, 2013. "On the approximation performance of fictitious play in finite games," International Journal of Game Theory, Springer, Springer, vol. 42(4), pages 1059-1083, November.
  20. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 76(1), pages 1-14.
  21. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp529, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  22. repec:hal:wpaper:hal-00817201 is not listed on IDEAS

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