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Learning Nash Equilibria

  • Dai, Darong
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    In the paper, we re-investigate the long run behavior of an adaptive learning process driven by the stochastic replicator dynamics developed by Fudenberg and Harris (1992). It is demonstrated that the Nash equilibrium will be the robust limit of the adaptive learning process as long as it is reachable for the learning dynamics in almost surely finite time. Doob’s martingale theory and Girsanov Theorem play very important roles in confirming the required assertion.

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    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40040.

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    Date of creation: 03 May 2012
    Date of revision:
    Handle: RePEc:pra:mprapa:40040
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    1. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
    2. Josef Hofbauer & Ed Hopkins, 2000. "Learning in Perturbed Asymmetric Games," ESE Discussion Papers 53, Edinburgh School of Economics, University of Edinburgh.
    3. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October.
    4. Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November.
    5. repec:oup:restud:v:66:y:1999:i:2:p:363-93 is not listed on IDEAS
    6. D. Fudenberg & C. Harris, 2010. "Evolutionary Dynamics with Aggregate Shocks," Levine's Working Paper Archive 496, David K. Levine.
    7. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
    8. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    9. A. Cabrales, 2010. "Stochastic Replicator Dynamics," Levine's Working Paper Archive 489, David K. Levine.
    10. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    11. Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August.
    12. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
    13. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    14. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
    15. Alan Beggs, 2002. "Stochastic evolution with slow learning," Economic Theory, Springer, vol. 19(2), pages 379-405.
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