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Stochastic uncoupled dynamics and Nash equilibrium

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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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Bibliographic 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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Keywords: Uncoupled; Nash equilibrium; stochastic dynamics; bounded recall;

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References

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  1. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780199269181, October.
  2. Fabrizio Germano & Gábor Lugosi, 2004. "Global Nash convergence of Foster and Young's regret testing," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 788, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Sergiu Hart & Andreu Mas-Colell, 2001. "Regret-Based Continuous-Time Dynamics," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp309, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised Apr 2003.
  4. 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.
  5. 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.
  6. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, Econometric Society, vol. 73(5), pages 1401-1430, 09.
  7. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information, EconWPA 9703006, EconWPA, revised 24 Mar 1997.
  8. 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.
  9. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(1), pages 5-39, March.
  10. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, Elsevier, vol. 65(2), pages 626-643, March.
  4. repec:hal:wpaper:hal-00817201 is not listed on IDEAS
  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. 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.
  7. George J. Mailath & Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring," PIER Working Paper Archive 08-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  8. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
  9. 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.
  10. Yakov Babichenko, 2014. "How long to Pareto efficiency?," International Journal of Game Theory, Springer, Springer, vol. 43(1), pages 13-24, February.
  11. 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.
  12. 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.
  13. 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.
  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. 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.
  16. 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.
  17. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, Elsevier, vol. 60(1), pages 135-154, July.
  18. Dean P Foster & Peyton Young, 2006. "Regret Testing Leads to Nash Equilibrium," Levine's Working Paper Archive 784828000000000676, David K. Levine.
  19. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Levine's Bibliography 843644000000000369, UCLA Department of Economics.
  20. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, Elsevier, vol. 76(1), pages 1-14.
  21. 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.
  22. Arieli, Itai & Babichenko, Yakov, 2012. "Average testing and Pareto efficiency," Journal of Economic Theory, Elsevier, Elsevier, vol. 147(6), pages 2376-2398.

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