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Fast convergence in evolutionary models: A Lyapunov approach

Author

Listed:
  • 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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    Cited by:

    1. Itai Arieli & Yakov Babichenko & Ron Peretz & H. Peyton Young, 2018. "The Speed of Innovation Diffusion," Economics Papers 2018-W06, Economics Group, Nuffield College, University of Oxford.
    2. D. Fudenberg & D. K. Levine, 2017. "Whither game theory? Towards a theory oflearning in games," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 5.
    3. Arieli, Itai & Babichenko, Yakov & Peretz, Ron & Young, H. Peyton, 2020. "The speed of innovation diffusion in social networks," LSE Research Online Documents on Economics 102538, London School of Economics and Political Science, LSE Library.
    4. David K Levine, 2022. "Phoenix From the Ashes: The Evolution of Mechanism Designers," Levine's Working Paper Archive 11694000000000141, David K. Levine.
    5. Itai Arieli & Yakov Babichenko & Ron Peretz & H. Peyton Young, 2020. "The Speed of Innovation Diffusion in Social Networks," Econometrica, Econometric Society, vol. 88(2), pages 569-594, March.

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    More about this item

    Keywords

    Hitting time; Learning model; Local interaction; Lyapunov function; Markov chain; Recency;
    All these keywords.

    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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