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Evolutionary fate of memory-one strategies in repeated prisoner’s dilemma game in structured populations

Author

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  • Xu-Sheng Liu

    (Institute of Computational Physics and Complex Systems, Lanzhou University)

  • Zhi-Xi Wu

    (Institute of Computational Physics and Complex Systems, Lanzhou University)

  • Michael Z. Q. Chen

    (School of Automation, Nanjing University of Science and Technology)

  • Jian-Yue Guan

    (Institute of Computational Physics and Complex Systems, Lanzhou University)

Abstract

We study evolutionary spatial prisoner’s dilemma game involving a one-step memory mechanism of the individuals whenever making strategy updating. In particular, during the process of strategy updating, each individual keeps in mind all the outcome of the action pairs adopted by himself and each of his neighbors in the last interaction, and according to which the individuals decide what actions they will take in the next round. Computer simulation results imply that win-stay-lose-shift like strategy win out of the memory-one strategy set in the stationary state. This result is robust in a large range of the payoff parameter, and does not depend on the initial state of the system. Furthermore, theoretical analysis with mean field and quasi-static approximation predict the same result. Thus, our studies suggest that win-stay-lose-shift like strategy is a stable dominant strategy in repeated prisoner’s dilemma game in homogeneous structured populations.

Suggested Citation

  • Xu-Sheng Liu & Zhi-Xi Wu & Michael Z. Q. Chen & Jian-Yue Guan, 2017. "Evolutionary fate of memory-one strategies in repeated prisoner’s dilemma game in structured populations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(7), pages 1-7, July.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:7:d:10.1140_epjb_e2017-80219-0
    DOI: 10.1140/epjb/e2017-80219-0
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    Cited by:

    1. Yang, Han-Xin & Sun, Lei, 2020. "Heterogeneous donation game in geographical small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Niloufar Najafian & Farhad Ferdowsi & Keivan Aghababaei Samani, 2021. "The effect of memory and vision range on cooperators dynamics in donation game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(5), pages 1-8, May.
    3. Fiaschi, Lorenzo & Cococcioni, Marco, 2021. "Non-Archimedean game theory: A numerical approach," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. Yang, Han-Xin & Yang, Jing, 2019. "Reputation-based investment strategy promotes cooperation in public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 886-893.

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    Keywords

    Statistical and Nonlinear Physics;

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