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Completely Uncoupled Dynamics and Nash Equilibria

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  • Yakov Babichenko

Abstract

A completely uncoupled dynamic is a repeated play of a game, where each period every player knows only his action set and the history of his own past actions and payoffs. One main result is that there exist no completely uncoupled dynamics with finite memory that lead to pure Nash equilibria (PNE) in almost all games possessing pure Nash equilibria. By "leading to PNE" we mean that the frequency of time periods at which some PNE is played converges to 1 almost surely. Another main result is that this is not the case when PNE is replaced by "Nash epsilon-equilibria": we exhibit a completely uncoupled dynamic with finite memory such that from some time on a Nash epsion-equilibrium is played almost surely.

Suggested Citation

  • Yakov Babichenko, 2010. "Completely Uncoupled Dynamics and Nash Equilibria," Discussion Paper Series dp529, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp529
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    References listed on IDEAS

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    1. 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.
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    7. 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..
    8. 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.
    9. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Levine's Bibliography 843644000000000369, UCLA Department of Economics.
    10. Yakov Babichenko, 2007. "Uncoupled Automata and Pure Nash Equilibria," Discussion Paper Series dp459, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    11. 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. Daskalakis, Constantinos & Deckelbaum, Alan & Kim, Anthony, 2015. "Near-optimal no-regret algorithms for zero-sum games," Games and Economic Behavior, Elsevier, vol. 92(C), pages 327-348.
    2. Marden, Jason R. & Shamma, Jeff S., 2012. "Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation," Games and Economic Behavior, Elsevier, vol. 75(2), pages 788-808.
    3. Marden, Jason R. & Shamma, Jeff S., 2015. "Game Theory and Distributed Control****Supported AFOSR/MURI projects #FA9550-09-1-0538 and #FA9530-12-1-0359 and ONR projects #N00014-09-1-0751 and #N0014-12-1-0643," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. 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.

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