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Completely Uncoupled Dynamics and Nash Equilibria

  • Yakov Babichenko
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    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.

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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp529.pdf
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    Paper provided by The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem in its series Discussion Paper Series with number dp529.

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    Length: 41 pages
    Date of creation: Jan 2010
    Date of revision:
    Handle: RePEc:huj:dispap:dp529
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    1. repec:oxf:wpaper:384 is not listed on IDEAS
    2. Hart, Sergiu & Mas-Colell, Andreu, 2006. "Stochastic uncoupled dynamics and Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 286-303, November.
    3. H. Peyton Young, 2007. "The Possible and the Impossible in Multi-Agent Learning," Economics Series Working Papers 304, University of Oxford, Department of Economics.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    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.
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