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Completely uncoupled dynamics and Nash equilibria

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  • Babichenko, Yakov

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.

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

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    6. , P. & , 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.
    7. 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.
    8. 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..
    9. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. Hart, Sergiu, 2011. "Commentary: Nash equilibrium and dynamics," Games and Economic Behavior, Elsevier, vol. 71(1), pages 6-8, January.
    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. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Nov 2023.
    2. Bervoets, Sebastian & Bravo, Mario & Faure, Mathieu, 2020. "Learning with minimal information in continuous games," Theoretical Economics, Econometric Society, vol. 15(4), November.
    3. Babichenko, Yakov & Rubinstein, Aviad, 2022. "Communication complexity of approximate Nash equilibria," Games and Economic Behavior, Elsevier, vol. 134(C), pages 376-398.
    4. Johannes Zschache, 2017. "The Explanation of Social Conventions by Melioration Learning," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 20(3), pages 1-1.
    5. Heinrich Nax, 2015. "Equity dynamics in bargaining without information exchange," Journal of Evolutionary Economics, Springer, vol. 25(5), pages 1011-1026, November.
    6. Foster, Dean P. & Hart, Sergiu, 2018. "Smooth calibration, leaky forecasts, finite recall, and Nash dynamics," Games and Economic Behavior, Elsevier, vol. 109(C), pages 271-293.
    7. 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.
    8. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    9. Johannes Zschache, 2016. "Melioration Learning in Two-Person Games," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-16, November.

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    More about this item

    Keywords

    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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