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Evolutionary prisoner's dilemma game on Barabási–Albert scale-free networks

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  • Wu, Zhi-Xi
  • Guan, Jian-Yue
  • Xu, Xin-Jian
  • Wang, Ying-Hai

Abstract

An evolutionary prisoner's dilemma game (PDG) with players located on Barabási–Albert scale-free networks (BASFN) with average connectivity 8 is studied in detail. The players are pure strategists and can adopt two strategies: either defect or cooperate. Several alternative update rules determining the evolution of each player's strategy are considered. Using Monte Carlo (MC) simulations we implemented both synchronous and asynchronous update dynamics to calculate the average density of cooperators ρC as a function of the temptation-to-defect b in the equilibrium state. For the sake of comparison, evolution of cooperative behavior on random regular graphs (RRG) and regular lattices (RL) with the same total size and average connectivity as BASFN are also investigated. We find the overall result that cooperation is sometimes inhibited and sometimes enhanced on the BASFN, with respect to the cases on the RRG and RL. The differences depend on the detailed evaluation function of the players’ success (average payoffs of the players in the present case), the different update rules that determine a player's future strategy, the synchronous and asynchronous events of strategy-updating, and also on the temptation to defect.

Suggested Citation

  • Wu, Zhi-Xi & Guan, Jian-Yue & Xu, Xin-Jian & Wang, Ying-Hai, 2007. "Evolutionary prisoner's dilemma game on Barabási–Albert scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 672-680.
    • Handle: RePEc:eee:phsmap:v:379:y:2007:i:2:p:672-680
    DOI: 10.1016/j.physa.2007.02.085
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    Citations

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    Cited by:

    1. 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.
    2. Liu, Run-Ran & Jia, Chun-Xiao & Rong, Zhihai, 2020. "Effects of strategy-updating cost on evolutionary spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. Wang, Xianjia & Lv, Shaojie, 2019. "The roles of particle swarm intelligence in the prisoner’s dilemma based on continuous and mixed strategy systems on scale-free networks," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 213-220.
    4. Dai, Qionglin & Li, Haihong & Cheng, Hongyan & Zhang, Mei & Yang, Junzhong, 2013. "The effects of nonlinear imitation probability on the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 53-58.
    5. Mao, Yajun & Rong, Zhihai & Wu, Zhi-Xi, 2021. "Effect of collective influence on the evolution of cooperation in evolutionary prisoner’s dilemma games," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    6. Li, Yixiao & Wang, Yi & Sheng, Jichuan, 2017. "The evolution of cooperation on geographical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 1-10.
    7. Wang, Lu & Ye, Shun-Qiang & Cheong, Kang Hao & Bao, Wei & Xie, Neng-gang, 2018. "The role of emotions in spatial prisoner’s dilemma game with voluntary participation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1396-1407.
    8. Liang, Rizhou & Zhang, Jiqiang & Zheng, Guozhong & Chen, Li, 2021. "Social hierarchy promotes the cooperation prevalence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    9. Ping Zhu & Guiyi Wei, 2014. "Stochastic Heterogeneous Interaction Promotes Cooperation in Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-10, April.
    10. Liangliang Chang & Zhipeng Zhang & Chengyi Xia, 2023. "Impact of Decision Feedback on Networked Evolutionary Game with Delays in Control Channel," Dynamic Games and Applications, Springer, vol. 13(3), pages 783-800, September.
    11. Chunyan Zhang & Jianlei Zhang & Guangming Xie & Long Wang & Matjaž Perc, 2011. "Evolution of Interactions and Cooperation in the Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-7, October.
    12. Sanz Nogales, Jose M. & Zazo, S., 2020. "Replicator based on imitation for finite and arbitrary networked communities," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    13. Angsheng Li & Xi Yong, 2015. "Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-24, February.
    14. Liu, Chao & Li, Rong, 2016. "Power-law distributed temporal heterogeneity of human activities promotes cooperation on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 93-100.
    15. 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.
    16. Li, Gang & Jin, Xiao-Gang & Song, Zhi-Huan, 2012. "Evolutionary game on a stochastic growth network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6664-6673.
    17. 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.

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