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Completely uncoupled dynamics and Nash equilibria

  • Babichenko, Yakov
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    Completely uncoupled dynamics are a repeated play of a game, where every period each player knows only his own action set and the history of his own past actions and payoffs; thus, he does not know anything about the other playerʼs actions and payoffs. The main contributions of the present paper are the following. First, there exist no completely uncoupled dynamics that lead to almost sure convergence of play to pure Nash equilibria in almost all games possessing pure Nash equilibria. Second, the above result does not hold for Nash ε-equilibrium: we exhibit completely uncoupled dynamics that lead to almost sure convergence of play to Nash ε-equilibrium.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0899825612000887
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    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 76 (2012)
    Issue (Month): 1 ()
    Pages: 1-14

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    Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:1-14
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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    1. Peyton Young, 2002. "Learning Hypothesis Testing and Nash Equilibrium," Economics Working Paper Archive 474, The Johns Hopkins University,Department of Economics.
    2. Sergiu Hart & Yishay Mansour, 2013. "How Long To Equilibrium? The Communication Complexity Of Uncoupled Equilibrium Procedures," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 10, pages 215-249 World Scientific Publishing Co. Pte. Ltd..
    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. 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. Dean Foster & H Peyton Young, 1999. "On the Impossibility of Predicting the Behavior of Rational Agents," Economics Working Paper Archive 423, The Johns Hopkins University,Department of Economics, revised Jun 2001.
    6. Sergiu Hart & Andreu Mas-Colell, 2004. "Stochastic Uncoupled Dynamics and Nash Equilibrium," Working Papers 174, Barcelona Graduate School of Economics.
    7. Foster, Dean P. & Young, H. Peyton, 2006. "Regret testing: learning to play Nash equilibrium without knowing you have an opponent," Theoretical Economics, Econometric Society, vol. 1(3), pages 341-367, September.
    8. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
    9. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    10. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
    11. Hart, Sergiu, 2011. "Commentary: Nash equilibrium and dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 6-8, January.
    12. Yakov Babichenko, 2010. "Uncoupled automata and pure Nash equilibria," International Journal of Game Theory, Springer, vol. 39(3), pages 483-502, July.
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