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On the elimination of dominated strategies in stochastic models of evolution with large populations

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  • Christoph Kuzmics

Abstract

A stochastic myopic best-reply dynamics is said to have property (W), for a given number of players n, if every pure weakly dominated strategy in every n-player game is eliminated in the long-run distribution of play induced by the dynamics. In this paper I give a necessary and sufficient condition that a dynamics has to satisfy in order for it to have property (W). The key determinant is found to be the sensitivity of the learning-rate to small payoff differences, inherent in the dynamics. If this sensitivity is higher than a certain cut-off, which depends on the number of players, then the dynamics satisfies property (W). If it is equal to or below that cut-off, then the dynamics does not satisfy property (W).
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Suggested Citation

  • Christoph Kuzmics, 2007. "On the elimination of dominated strategies in stochastic models of evolution with large populations," Levine's Bibliography 321307000000000943, UCLA Department of Economics.
    • Handle: RePEc:cla:levrem:321307000000000943
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    2. Dai Zusai, 2018. "Distributional stability and deterministic equilibrium selection under heterogeneous evolutionary dynamics," Papers 1805.04895, arXiv.org.
    3. Heller, Yuval & Kuzmics, Christoph, 2020. "Communication, Renegotiation and Coordination with Private Values (Extended Version)," MPRA Paper 102926, University Library of Munich, Germany, revised 26 Jul 2021.
    4. Christoph Kuzmics & Daniel Rodenburger, 2020. "A case of evolutionarily stable attainable equilibrium in the laboratory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 685-721, October.
    5. Bernergård, Axel & Mohlin, Erik, 2019. "Evolutionary selection against iteratively weakly dominated strategies," Games and Economic Behavior, Elsevier, vol. 117(C), pages 82-97.
    6. Xu, Hedong & Fan, Suohai & Tian, Cunzhi & Xiao, Xinrong, 2019. "Effect of strategy-assortativity on investor sharing games in the market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 211-225.
    7. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    8. Christopher Kah & Markus Walzl, 2015. "Stochastic Stability in a Learning Dynamic with Best Response to Noisy Play," Working Papers 2015-15, Faculty of Economics and Statistics, Universität Innsbruck.
    9. Dai Zusai, 2018. "Tempered best response dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 1-34, March.

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