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Fixation of strategies with the Moran and Fermi processes in evolutionary games

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  • Liu, Xuesong
  • He, Mingfeng
  • Kang, Yibin
  • Pan, Qiuhui

Abstract

A model of stochastic evolutionary game dynamics with finite population was built. It combines the standard Moran and Fermi rules with two strategies cooperation and defection. We obtain the expressions of fixation probabilities and fixation times. The one-third rule which has been found in the frequency dependent Moran process also holds for our model. We obtain the conditions of strategy being an evolutionarily stable strategy in our model, and then make a comparison with the standard Moran process. Besides, the analytical results show that compared with the standard Moran process, fixation occurs with higher probabilities under a prisoner’s dilemma game and coordination game, but with lower probabilities under a coexistence game. The simulation result shows that the fixation time in our mixed process is lower than that in the standard Fermi process. In comparison with the standard Moran process, fixation always takes more time on average in spatial populations, regardless of the game. In addition, the fixation time decreases with the growth of the number of neighbors.

Suggested Citation

  • Liu, Xuesong & He, Mingfeng & Kang, Yibin & Pan, Qiuhui, 2017. "Fixation of strategies with the Moran and Fermi processes in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 336-344.
    • Handle: RePEc:eee:phsmap:v:484:y:2017:i:c:p:336-344
    DOI: 10.1016/j.physa.2017.04.154
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    References listed on IDEAS

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    1. 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.
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    3. repec:hhs:iuiwop:487 is not listed on IDEAS
    4. Laura Hindersin & Arne Traulsen, 2015. "Most Undirected Random Graphs Are Amplifiers of Selection for Birth-Death Dynamics, but Suppressors of Selection for Death-Birth Dynamics," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-14, November.
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    Cited by:

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    3. Gu, Cuiling & Wang, Xianjia & Zhao, Jinhua & Ding, Rui & He, Qilong, 2020. "Evolutionary game dynamics of Moran process with fuzzy payoffs and its application," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    4. Hong, Lijun & Geng, Yini & Du, Chunpeng & Shen, Chen & Shi, Lei, 2021. "Average payoff-driven or imitation? A new evidence from evolutionary game theory in finite populations," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    5. Paul F. Slade, 2019. "Dominant Cubic Coefficients of the ‘1/3-Rule’ Reduce Contest Domains," Mathematics, MDPI, vol. 7(6), pages 1-11, May.
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    7. Wang, Si-Yi & Wang, Qing-Lian & Zhang, Xiao-Wei & Wang, Rui-Wu, 2023. "Evolutionary cooperation dynamics of combining imitation and super-rational aspiration induced strategy updating," Applied Mathematics and Computation, Elsevier, vol. 456(C).

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