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Enhancement of cooperation in prisoner’s dilemma game on weighted lattices

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  • Xia, Cheng-yi
  • Ma, Zhi-qin
  • Wang, Yi-ling
  • Wang, Jin-song
  • Chen, Zeng-qiang

Abstract

We introduce the vertex weight into the spatial prisoners’ dilemma game to investigate the evolution of cooperation. Each player on a square lattice is assigned to a particular weight followed by three types of distributions, which include the exponential, power-law and uniform ones. Compared with the traditional version, we find that the cooperation level is markedly enhanced under the weighted square lattice. For most ranges of b, the highest cooperation level can be obtained under the uniform distribution, while power-law distribution usually leads to the lowest cooperation. The distributed weight can produce a heavy heterogeneity among the individuals’ payoff, some cooperators with higher weight will foster the cooperative clusters and even spread the cooperation strategy around the clusters, while defectors have no such advantages. In addition, we still investigate the impact of the amplitude of undulation of weight distribution on the cooperation, and the non-monotonic behavior about b is observed. Finally, the influence of noise on the cooperation is also studied for these types of distribution of weight. To some extent, our weighted scheme can characterize the difference or diversity of players, which will be beneficial to further understand the role of individuals during the evolution of cooperation.

Suggested Citation

  • Xia, Cheng-yi & Ma, Zhi-qin & Wang, Yi-ling & Wang, Jin-song & Chen, Zeng-qiang, 2011. "Enhancement of cooperation in prisoner’s dilemma game on weighted lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4602-4609.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4602-4609
    DOI: 10.1016/j.physa.2011.06.064
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    Citations

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    Cited by:

    1. Kohei Miyaji & Jun Tanimoto & Zhen Wang & Aya Hagishima & Naoki Ikegaya, 2013. "Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    2. Xia, Chengyi & Miao, Qin & Zhang, Juanjuan, 2013. "Impact of neighborhood separation on the spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 51(C), pages 22-30.
    3. Cui, Guang-Hai & Wang, Zhen & Yang, Yan-Cun & Tian, Sheng-Wen & Yue, Jun, 2018. "Heterogeneous game resource distributions promote cooperation in spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1191-1200.
    4. Ding, Chenxi & Wang, Juan & Zhang, Ying, 2016. "Impact of self interaction on the evolution of cooperation in social spatial dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 393-399.
    5. Chen, Zhi-Gang & Wang, Tao & Xiao, De-Gui & Xu, Yin, 2013. "Can remembering history from predecessor promote cooperation in the next generation?," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 59-68.
    6. Sun, Jiaqin & Fan, Ruguo & Luo, Ming & Zhang, Yingqing & Dong, Lili, 2018. "The evolution of cooperation in spatial prisoner’s dilemma game with dynamic relationship-based preferential learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 598-611.
    7. Wang, Chengjiang & Wang, Li & Wang, Juan & Sun, Shiwen & Xia, Chengyi, 2017. "Inferring the reputation enhances the cooperation in the public goods game on interdependent lattices," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 18-29.
    8. Wu, Jianshe & Hou, Yanqiao & Jiao, Licheng & Li, Huijie, 2014. "Community structure inhibits cooperation in the spatial prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 169-179.
    9. Changbing Tang & Zhen Wang & Xiang Li, 2014. "Moderate Intra-Group Bias Maximizes Cooperation on Interdependent Populations," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-7, February.
    10. Tian, Lin-Lin & Li, Ming-Chu & Lu, Kun & Zhao, Xiao-Wei & Wang, Zhen, 2013. "The influence of age-driven investment on cooperation in spatial public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 65-70.
    11. Xia, Chengyi & Wang, Juan & Wang, Li & Sun, Shiwen & Sun, Junqing & Wang, Jinsong, 2012. "Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1239-1245.
    12. Li, Hong-yang & Xiao, Jian & Li, Yu-meng & Wang, Zhen, 2013. "Effects of neighborhood type and size in spatial public goods game on diluted lattice," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 145-153.
    13. Zheng, Junjun & He, Yujie & Ren, Tianyu & Huang, Yongchao, 2022. "Evolution of cooperation in public goods games with segregated networks and periodic invasion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    14. Wang, Lei & Xia, Chengyi & Wang, Li & Zhang, Ying, 2013. "An evolving Stag-Hunt game with elimination and reproduction on regular lattices," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 69-76.
    15. Zhang, Yingchao & Ning, Hongyun & Wang, Juan & Xia, Chengyi, 2017. "Coveting the successful neighbor promotes the cooperation for the spatial public goods game on two-layered lattices," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 29-37.
    16. Wu, Yu’e & Zhang, Zhipeng & Wang, Xinyu & Chang, Shuhua, 2019. "Impact of probabilistic incentives on the evolution of cooperation in complex topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 307-314.
    17. Zhou, Tianwei & Ding, Shuai & Fan, Wenjuan & Wang, Hao, 2016. "An improved public goods game model with reputation effect on the spatial lattices," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 130-135.
    18. Quan, Ji & Yang, Xiukang & Wang, Xianjia, 2018. "Spatial public goods game with continuous contributions based on Particle Swarm Optimization learning and the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 973-983.
    19. Wang, Lei & Wang, Juan & Guo, Baohong & Ding, Shuai & Li, Yukun & Xia, Chengyi, 2014. "Effects of benefit-inspired network coevolution on spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 9-16.
    20. Zhang, Shuhua & Zhang, Zhipeng & Wu, Yu’e & Yan, Ming & Li, Yu, 2019. "Strategy preference promotes cooperation in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 181-188.
    21. Zhu, Song-Ping & Lian, Guang-Hua, 2015. "Pricing forward-start variance swaps with stochastic volatility," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 920-933.
    22. Yang, Xiqing & Zhang, Feng & Wang, Wanxiong, 2019. "Predation promotes cooperation in Prisoner’s dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 20-24.
    23. Liu, Yongkui & Chen, Xiaojie & Zhang, Lin & Tao, Fei & Wang, Long, 2012. "Does migration cost influence cooperation among success-driven individuals?," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1301-1308.
    24. Jin, Jiahua & Chu, Chen & Shen, Chen & Guo, Hao & Geng, Yini & Jia, Danyang & Shi, Lei, 2018. "Heterogeneous fitness promotes cooperation in the spatial prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 141-146.

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