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Completely uncoupled dynamics and Nash equilibria


  • Babichenko, Yakov


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.

Suggested Citation

  • Babichenko, Yakov, 2012. "Completely uncoupled dynamics and Nash equilibria," Games and Economic Behavior, Elsevier, vol. 76(1), pages 1-14.
  • Handle: RePEc:eee:gamebe:v:76:y:2012:i:1:p:1-14
    DOI: 10.1016/j.geb.2012.06.004

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. Hart, Sergiu & Mas-Colell, Andreu, 2006. "Stochastic uncoupled dynamics and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 286-303, November.
    4. 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.
    5. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    6. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    7. 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..
    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. 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.
    10. Hart, Sergiu, 2011. "Commentary: Nash equilibrium and dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 6-8, January.
    11. Yakov Babichenko, 2010. "Uncoupled automata and pure Nash equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 483-502, July.
    12. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
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    Cited by:

    1. Nax, Heinrich H., 2015. "Equity dynamics in bargaining without information exchange," LSE Research Online Documents on Economics 65426, London School of Economics and Political Science, LSE Library.
    2. Heinrich Nax, 2015. "Equity dynamics in bargaining without information exchange," Journal of Evolutionary Economics, Springer, vol. 25(5), pages 1011-1026, November.

    More about this item


    Completely uncoupled dynamics; Nash equilibria;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games


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