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Completely uncoupled dynamics and Nash equilibria

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  • Babichenko, Yakov
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    Abstract

    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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    Bibliographic Info

    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

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

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    Keywords: Completely uncoupled dynamics; Nash equilibria;

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    1. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
    2. 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.
    3. Yakov Babichenko, 2010. "Uncoupled automata and pure Nash equilibria," International Journal of Game Theory, Springer, vol. 39(3), pages 483-502, July.
    4. Hart, Sergiu & Mas-Colell, Andreu, 2006. "Stochastic uncoupled dynamics and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 286-303, November.
    5. Dean P. Foster & H. Peyton Young, 2001. "On the Impossibility of Predicting the Behavior of Rational Agents," Working Papers 01-08-039, Santa Fe Institute.
    6. 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.
    7. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
    8. 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.
    9. Hart, Sergiu, 2011. "Commentary: Nash equilibrium and dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 6-8, January.
    10. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    11. 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.
    12. 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.
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