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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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References

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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. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  3. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
  4. 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.
  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.
  6. 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.
  7. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
  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.
  10. 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.
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Citations

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Cited by:
  1. 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.
  2. Hart, Sergiu & Mansour, Yishay, 2010. "How long to equilibrium? The communication complexity of uncoupled equilibrium procedures," Games and Economic Behavior, Elsevier, vol. 69(1), pages 107-126, May.
  3. 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.
  4. George Mailath & Wojciech Olszewski, 2008. "Folk theorems with Bounded Recall under(Almost) Perfect Monitoring," Discussion Papers 1462, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. 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.
  6. 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.
  7. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
  8. 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, issue 5, pages 10-27.
  9. Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series dp600, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  10. 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, vol. 42(4), pages 1059-1083, November.
  11. Arieli, Itai & Babichenko, Yakov, 2012. "Average testing and Pareto efficiency," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2376-2398.
  12. repec:hal:wpaper:hal-00817201 is not listed on IDEAS
  13. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
  14. 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.
  15. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Levine's Bibliography 843644000000000369, UCLA Department of Economics.
  16. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Discussion Paper Series dp459, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  17. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  18. Itai Arieli & H Peyton Young, 2011. "Fast Convergence in Population Games," Economics Series Working Papers 570, University of Oxford, Department of Economics.
  19. Pradelski, Bary S.R. & Young, H. Peyton, 2012. "Learning efficient Nash equilibria in distributed systems," Games and Economic Behavior, Elsevier, vol. 75(2), pages 882-897.
  20. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
  21. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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