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Stochastic Uncoupled Dynamics and Nash Equilibrium

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  • Sergiu Hart
  • Andreu Mas-Colell

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

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000466.

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Date of creation: 17 Sep 2004
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Handle: RePEc:cla:levrem:122247000000000466

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  1. 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.
  2. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
  3. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
  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. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
  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.
  7. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
  8. Hart, Sergiu & Mas-Colell, Andreu, 2003. "Regret-based continuous-time dynamics," Games and Economic Behavior, Elsevier, vol. 45(2), pages 375-394, November.
  9. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
  10. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
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Citations

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Cited by:
  1. 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.
  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. 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.
  4. 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.
  5. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Levine's Bibliography 843644000000000369, UCLA Department of Economics.
  6. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
  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. 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.
  9. repec:hal:wpaper:hal-00817201 is not listed on IDEAS
  10. Yakov Babichenko, 2012. "Best-Reply Dynamics in Large Anonymous Games," Discussion Paper Series dp600, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  11. Arieli, Itai & Babichenko, Yakov, 2012. "Average testing and Pareto efficiency," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2376-2398.
  12. Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
  13. 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.
  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. 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," Discussion Paper Series dp459, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  17. 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.
  18. Itai Arieli & H Peyton Young, 2011. "Fast Convergence in Population Games," Economics Series Working Papers 570, University of Oxford, Department of Economics.
  19. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
  20. Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  21. 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.

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