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Evolutionary dynamics of N-person snowdrift game with two thresholds in well-mixed and structured populations

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  • Pi, Jinxiu
  • Wang, Chun
  • Zhou, Die
  • Tang, Wei
  • Yang, Guanghui

Abstract

In this paper, to state the necessary and the critical number of cooperators for completing the snow shoveling, we investigate the evolutionary dynamics of an N-person snowdrift game with two thresholds in well-mixed populations and structured populations. Firstly, we discuss the effects of these thresholds on equilibria in infinite well-mixed populations by applying the replicator equation, and observe that there exist three types of equilibria with the variations of parameters. Secondly, we study the game in finite well-mixed populations by means of the Markov process, and find that the evolutionary results converge to those in infinite population as the finite population size increases. Finally, we explore such a game in structured populations by using the pair approximation approach, and derive the dynamical equation under weak selection, which is ignored in the previous work. Results present that structured populations can create more complicated behaviors of the cooperative dynamics, and to some extent facilitate cooperation compared with well-mixed populations. Our work helpfully provides a theoretical approximation for the N-person snowdrift game in more complicated scenarios.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924001449
    DOI: 10.1016/j.chaos.2024.114593
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    References listed on IDEAS

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    1. Hu, Xiang & Liu, Xingwen, 2021. "Unfixed-neighbor-mechanism promotes cooperation in evolutionary snowdrift game on lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    3. Su, Qi & Li, Aming & Wang, Long, 2017. "Spatial structure favors cooperative behavior in the snowdrift game with multiple interactive dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 299-306.
    4. Xiaofeng Wang, 2021. "Costly Participation and The Evolution of Cooperation in the Repeated Public Goods Game," Dynamic Games and Applications, Springer, vol. 11(1), pages 161-183, March.
    5. Wang, Jianwei & He, Jialu & Yu, Fengyuan, 2021. "Heterogeneity of reputation increment driven by individual influence promotes cooperation in spatial social dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    6. Wang, Qiang & He, Nanrong & Chen, Xiaojie, 2018. "Replicator dynamics for public goods game with resource allocation in large populations," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 162-170.
    7. Yongkui Liu & Xiaojie Chen & Lin Zhang & Long Wang & Matjaž Perc, 2012. "Win-Stay-Lose-Learn Promotes Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 7(2), pages 1-8, February.
    8. Shi, Yong-Dong & Zhong, Li-Xin & Xu, Wen-Juan, 2013. "Effects of group sensitivity on cooperation in N-person snowdrift game with dynamic grouping," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 132-138.
    9. 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.
    10. 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.
    11. Li, Kun & Mao, Yizhou & Wei, Zhenlin & Cong, Rui, 2021. "Pool-rewarding in N-person snowdrift game," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    12. 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).
    13. Yang, Zhengzhi & Zheng, Lei & Perc, Matjaž & Li, Yumeng, 2024. "Interaction state Q-learning promotes cooperation in the spatial prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    14. Boyu Zhang & Cong Li & Yi Tao, 2016. "Evolutionary Stability and the Evolution of Cooperation on Heterogeneous Graphs," Dynamic Games and Applications, Springer, vol. 6(4), pages 567-579, December.
    15. Chu, Chen & Liu, Jinzhuo & Shen, Chen & Jin, Jiahua & Tang, Yunxuan & Shi, Lei, 2017. "Coevolution of game strategy and link weight promotes cooperation in structured population," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 28-32.
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