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Selection intensity and risk-dominant strategy: A two-strategy stochastic evolutionary game dynamics in finite population

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  • Yu, Jie-Ru
  • Liu, Xue-Lu
  • Zheng, Xiu-Deng
  • Tao, Yi

Abstract

Stochastic evolutionary game dynamics with weak selection in finite population has been studied and it has been used to explain the emergence of cooperation. In this paper, following the previous studies, the diffusion approximation of a two-strategy stochastic evolutionary game dynamics in finite population that includes a small mutation rate between two strategies is investigated, where we assume that these two strategies are both strict Nash equilibrium (NE). Our main goal is to partially reveal the effect of selection intensity on the stochastic evolutionary game dynamics. Through the analysis of potential function of the stationary distribution, our main result shows that for all possible situations with that the selection intensity is not zero (that includes the strong selection), if a strategy is a risk-dominant NE, then its expected fitness with respect to the stationary distribution must be larger than that of other strategy. This result not only extends the previous results but also provides some useful insights for understanding the significance of selection intensity in stochastic evolutionary game dynamics in finite population.

Suggested Citation

  • Yu, Jie-Ru & Liu, Xue-Lu & Zheng, Xiu-Deng & Tao, Yi, 2017. "Selection intensity and risk-dominant strategy: A two-strategy stochastic evolutionary game dynamics in finite population," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 1-7.
    • Handle: RePEc:eee:apmaco:v:297:y:2017:i:c:p:1-7
    DOI: 10.1016/j.amc.2016.10.039
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    References listed on IDEAS

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    1. Xiudeng Zheng & Ross Cressman & Yi Tao, 2011. "The Diffusion Approximation of Stochastic Evolutionary Game Dynamics: Mean Effective Fixation Time and the Significance of the One-Third Law," Dynamic Games and Applications, Springer, vol. 1(3), pages 462-477, September.
    2. Ken Binmore & Larry Samuelson & Petyon Young, 2003. "Equilibrium Selection in Bargaining Models," Levine's Bibliography 506439000000000466, UCLA Department of Economics.
    3. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    4. Binmore, Ken & Samuelson, Larry & Young, Peyton, 2003. "Equilibrium selection in bargaining models," Games and Economic Behavior, Elsevier, vol. 45(2), pages 296-328, November.
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    Cited by:

    1. Jun Du & Jiejie Li & Jiaxin Li & Weiduo Li, 2023. "Competition–cooperation mechanism of online supply chain finance based on a stochastic evolutionary game," Operational Research, Springer, vol. 23(3), pages 1-28, September.
    2. Lin, XuXun & Yuan, PengCheng, 2018. "A dynamic parking charge optimal control model under perspective of commuters’ evolutionary game behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1096-1110.

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