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Evolutionary games on networks: Phase transition, quasi-equilibrium, and mathematical principles

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  • Cheng, Jiangjiang
  • Mei, Wenjun
  • Su, Wei
  • Chen, Ge

Abstract

The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such “stable” cooperation ratios obtained via approximate methods might not be actually stable, but correspond to quasi-equilibriums instead. We find that various classic game models, like the evolutionary snowdrift game, evolutionary prisoner’s dilemma, and spatial public goods game on square lattices and scale-free networks, exhibit the phase transition in convergence time to the equilibrium state. Moreover, mathematical principles are provided to explain the phase transition of convergence time and quasi-equilibrium of cooperation ratio. The findings explain why and when cooperation and defection have a long-term coexistence.

Suggested Citation

  • Cheng, Jiangjiang & Mei, Wenjun & Su, Wei & Chen, Ge, 2023. "Evolutionary games on networks: Phase transition, quasi-equilibrium, and mathematical principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    • Handle: RePEc:eee:phsmap:v:611:y:2023:i:c:s037843712300002x
    DOI: 10.1016/j.physa.2023.128447
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    References listed on IDEAS

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    1. Aming Li & Lei Zhou & Qi Su & Sean P. Cornelius & Yang-Yu Liu & Long Wang & Simon A. Levin, 2020. "Evolution of cooperation on temporal networks," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    2. Marco Alberto Javarone, 2016. "Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-6, February.
    3. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    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. Kate Donahue & Oliver P. Hauser & Martin A. Nowak & Christian Hilbe, 2020. "Evolving cooperation in multichannel games," Nature Communications, Nature, vol. 11(1), pages 1-9, December.
    6. 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.
    7. Christian Hilbe & Štěpán Šimsa & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Evolution of cooperation in stochastic games," Nature, Nature, vol. 559(7713), pages 246-249, July.
    8. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    9. Chiong, Raymond & Kirley, Michael, 2012. "Random mobility and the evolution of cooperation in spatial N-player iterated Prisoner’s Dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 3915-3923.
    10. Ren, Guangming & Wang, Xingyuan, 2014. "Robustness of cooperation in memory-based prisoner’s dilemma game on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 40-46.
    11. Xu, Yan & Feng, Meiling & Zhu, Yuying & Xia, Chengyi, 2022. "Multi-player snowdrift game on scale-free simplicial complexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    12. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    13. Marco Alberto Javarone, 2016. "Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-6, February.
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