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Fast convergence in evolutionary models: A Lyapunov approach

Author

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  • Ellison, Glenn
  • Fudenberg, Drew
  • Imhof, Lorens A.

Abstract

Evolutionary models in which N players are repeatedly matched to play a game have “fast convergence” to a set A if the models both reach A quickly and leave A slowly, where “quickly” and “slowly” refer to whether the expected hitting and exit times remain bounded when N tends to infinity. We provide simple and general Lyapunov criteria which are sufficient for reaching quickly and leaving slowly. We use these criteria to determine aspects of learning models that promote fast convergence.

Suggested Citation

  • Ellison, Glenn & Fudenberg, Drew & Imhof, Lorens A., 2016. "Fast convergence in evolutionary models: A Lyapunov approach," Journal of Economic Theory, Elsevier, vol. 161(C), pages 1-36.
  • Handle: RePEc:eee:jetheo:v:161:y:2016:i:c:p:1-36
    DOI: 10.1016/j.jet.2015.10.008
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    References listed on IDEAS

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    Cited by:

    1. D. Fudenberg & D. K. Levine., 2017. "Whither game theory? Towards a theory of learning in games," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 5.

    More about this item

    Keywords

    Hitting time; Learning model; Local interaction; Lyapunov function; Markov chain; Recency;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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