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Stochastic Evolutionary Game Dynamics and Their Selection Mechanisms

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  • Xing Gao
  • Weijun Zhong
  • Shue Mei

Abstract

An underlying assumption of deterministic evolutionary game dynamics is that all individuals interact with each other in infinite populations, which seems unrealistic since in reality populations are always finite in size and even disturbed by stochastic effects and random drift. Developed in the context of finite populations and described by finite state Markov processes, stochastic evolutionary game dynamics have received much attention recently. However, the relationship between two types of evolutionary dynamics so far has failed to be thoroughly understood. In this paper, we establish several classes of selection mechanisms in large populations under which corresponding stochastic evolutionary dynamics approach the imitative dynamic (including the replicator dynamic), the impartial pairwise comparison dynamic (including the Smith dynamic) and the separable excess payoff dynamic (including the Brown–von Neumann–Nash dynamic) respectively in adjusted forms. In other words, we present intuitive interpretations from a statistical perspective for these deterministic dynamics by constructing their microscopic foundations in settings with finite but large populations. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Xing Gao & Weijun Zhong & Shue Mei, 2013. "Stochastic Evolutionary Game Dynamics and Their Selection Mechanisms," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 233-247, February.
    • Handle: RePEc:kap:compec:v:41:y:2013:i:2:p:233-247
    DOI: 10.1007/s10614-012-9320-4
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    References listed on IDEAS

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    Cited by:

    1. Xinmin Liu & Kangkang Lin & Lei Wang & Hongkun Zhang, 2021. "Stochastic Evolutionary Game Analysis Between Special Committees and CEO: Incentive and Supervision," Dynamic Games and Applications, Springer, vol. 11(3), pages 538-555, September.
    2. Jianguo Ren & Yonghong Xu, 2014. "Modelling the Effects of Selection Temperature and Mutation on the Prisoner’s Dilemma Game on a Complete Oriented Star," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-9, October.
    3. Konstantin Avrachenkov & Vivek S. Borkar, 2019. "Metastability in Stochastic Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 9(2), pages 366-390, June.
    4. Robert Jump, 2013. "Results on the Stability of a Simple Wage Posting Model," Studies in Economics 1319, School of Economics, University of Kent.
    5. Gao, Xing & Zhong, Weijun & Mei, Shue, 2013. "A game-theory approach to configuration of detection software with decision errors," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 35-43.

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    More about this item

    Keywords

    Stochastic evolutionary game dynamics; Finite population; Selection mechanisms; Coordination game; C73;
    All these keywords.

    JEL classification:

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

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