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Cooperative behavior and phase transitions in co-evolving stag hunt game

Author

Listed:
  • Zhang, W.
  • Li, Y.S.
  • Xu, C.
  • Hui, P.M.

Abstract

Cooperative behavior and different phases in a co-evolving network dynamics based on the stag hunt game is studied. The dynamical processes are parameterized by a payoff r that tends to promote non-cooperative behavior and a probability q for a rewiring attempt that could isolate the non-cooperators. The interplay between the parameters leads to different phases. Detailed simulations and a mean field theory are employed to reveal the properties of different phases. For small r, the cooperators are the majority and form a connected cluster while the non-cooperators increase with q but remain isolated over the whole range of q, and it is a static phase. For sufficiently large r, cooperators disappear in an intermediate range qL≤q≤qU and a dynamical all-non-cooperators phase results. For q>qU, a static phase results again. A mean field theory based on how the link densities change in time by the co-evolving dynamics is constructed. The theory gives a phase diagram in the q–r parameter space that is qualitatively in agreement with simulation results. The sources of discrepancies between theory and simulations are discussed.

Suggested Citation

  • Zhang, W. & Li, Y.S. & Xu, C. & Hui, P.M., 2016. "Cooperative behavior and phase transitions in co-evolving stag hunt game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 161-169.
    • Handle: RePEc:eee:phsmap:v:443:y:2016:i:c:p:161-169
    DOI: 10.1016/j.physa.2015.09.047
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    Citations

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    Cited by:

    1. Yunsheng Deng & Jihui Zhang, 2022. "The choice-decision based on memory and payoff favors cooperation in stag hunt game on interdependent networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-13, February.
    2. Xin, C. & Yang, G. & Huang, J.P., 2017. "Ising game: Nonequilibrium steady states of resource-allocation systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 666-673.
    3. Wang, Chaoqian & Pan, Qiuhui & Ju, Xinxiang & He, Mingfeng, 2021. "Public goods game with the interdependence of different cooperative strategies," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Takesue, Hirofumi, 2019. "Effects of updating rules on the coevolving prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 399-408.
    5. Yuan, Hairui & Meng, Xinzhu, 2022. "Replicator dynamics of the Hawk-Dove game with different stochastic noises in infinite populations," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. Wang, Chaoqian & Lin, Zongzhe & Rothman, Dale S., 2022. "Public goods game on coevolving networks driven by the similarity and difference of payoff," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Shu, Feng, 2020. "A win-switch-lose-stay strategy promotes cooperation in the evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    8. Dong, Yukun & Xu, Hedong & Fan, Suohai, 2019. "Memory-based stag hunt game on regular lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 247-255.

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