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Cooperation in N-person evolutionary snowdrift game in scale-free Barabási–Albert networks

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  • Lee, K.H.
  • Chan, Chun-Him
  • Hui, P.M.
  • Zheng, Da-Fang

Abstract

Cooperation in the N-person evolutionary snowdrift game (NESG) is studied in scale-free Barabási–Albert (BA) networks. Due to the inhomogeneity of the network, two versions of NESG are proposed and studied. In a model where the size of the competing group varies from agent to agent, the fraction of cooperators drops as a function of the payoff parameter. The networking effect is studied via the fraction of cooperative agents for nodes with a particular degree. For small payoff parameters, it is found that the small-k agents are dominantly cooperators, while large-k agents are of non-cooperators. Studying the spatial correlation reveals that cooperative agents will avoid to be nearest neighbors and the correlation disappears beyond the next-nearest neighbors. The behavior can be explained in terms of the networking effect and payoffs. In another model with a fixed size of competing groups, the fraction of cooperators could show a non-monotonic behavior in the regime of small payoff parameters. This non-trivial behavior is found to be a combined effect of the many agents with the smallest degree in the BA network and the increasing fraction of cooperators among these agents with the payoff for small payoffs.

Suggested Citation

  • Lee, K.H. & Chan, Chun-Him & Hui, P.M. & Zheng, Da-Fang, 2008. "Cooperation in N-person evolutionary snowdrift game in scale-free Barabási–Albert networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5602-5608.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:22:p:5602-5608
    DOI: 10.1016/j.physa.2008.05.045
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
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    1. 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).
    2. Pi, Jinxiu & Yang, Guanghui & Yang, Hui, 2022. "Evolutionary dynamics of cooperation in N-person snowdrift games with peer punishment and individual disguise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    3. Geng, Yini & Shen, Chen & Guo, Hao & Chu, Chen & Yu, Dalei & Shi, Lei, 2017. "Historical payoff promotes cooperation in voluntary prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 145-149.
    4. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    5. Pi, Jinxiu & Wang, Chun & Zhou, Die & Tang, Wei & Yang, Guanghui, 2024. "Evolutionary dynamics of N-person snowdrift game with two thresholds in well-mixed and structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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