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Spatial social dilemmas: Dilution, mobility and grouping effects with imitation dynamics

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  • Vainstein, Mendeli H.
  • Arenzon, Jeferson J.

Abstract

We present an extensive, systematic study of the Prisoner’s Dilemma and Snowdrift games on a square lattice under a synchronous, noiseless imitation dynamics. We show that for both the occupancy of the network and the (random) mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear. We analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice. We point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results.

Suggested Citation

  • Vainstein, Mendeli H. & Arenzon, Jeferson J., 2014. "Spatial social dilemmas: Dilution, mobility and grouping effects with imitation dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 145-157.
    • Handle: RePEc:eee:phsmap:v:394:y:2014:i:c:p:145-157
    DOI: 10.1016/j.physa.2013.09.032
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    Citations

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    Cited by:

    1. Alessandra F. Lütz & Marco A. Amaral & Lucas Wardil, 2021. "Acculturation and the evolution of cooperation in spatial public goods games," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(11), pages 1-11, November.
    2. Shilin Xiao & Liming Zhang & Haihong Li & Qionglin Dai & Junzhong Yang, 2022. "Environment-driven migration enhances cooperation in evolutionary public goods games," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(4), pages 1-9, April.
    3. Li, Yan & Ye, Hang & Zhang, Hong, 2016. "Evolution of cooperation driven by social-welfare-based migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 48-56.
    4. Flores, Lucas S. & Amaral, Marco A. & Vainstein, Mendeli H. & Fernandes, Heitor C.M., 2022. "Cooperation in regular lattices," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    5. Ren, Yizhi & Chen, Xiangyu & Wang, Zhen & Shi, Benyun & Cui, Guanghai & Wu, Ting & Choo, Kim-Kwang Raymond, 2018. "Neighbor-considered migration facilitates cooperation in prisoner’s dilemma games," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 95-105.

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