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Learning Nash Equilibria

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  • Dai, Darong

Abstract

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.

Suggested Citation

  • Dai, Darong, 2012. "Learning Nash Equilibria," MPRA Paper 40040, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:40040
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Stochastic replicator dynamics; Adaptive learning; Nash equilibria; Global convergence; Robustness;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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