IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v505y2018icp973-983.html
   My bibliography  Save this article

Spatial public goods game with continuous contributions based on Particle Swarm Optimization learning and the evolution of cooperation

Author

Listed:
  • Quan, Ji
  • Yang, Xiukang
  • Wang, Xianjia

Abstract

How to explain the evolution of cooperation in social dilemmas has plagued the theorists of various disciplines. In this paper, we study the public goods game on two structured populations, assuming that each individual can make a continuous contribution in its strategy space. In our model, individuals have memory and imitation ability. They can remember their best history strategy and learn their best neighbors by obtaining the local information. We use the particle swarm optimization (PSO) algorithm to simulate the learning process of individuals. Two network structures of the square lattice and the nearest-neighbor coupled network are considered respectively. We investigate the combined effects of memory, the invest enhancement and the network structure on the average cooperation level of the population. By simulation experiments, we find that the PSO learning mechanism can promote the evolution of cooperation in a large range of parameters under both of the two kinds of networks. Compared with the square lattice network, the nearest-neighbor coupled network can promote the evolution of cooperation in a larger parameter scope. Compared with the Fermi rule and the Genetic Algorithm learning, the PSO learning can induce the population achieve a wider range of cooperation level, which makes it possible to achieve a higher level of cooperation. These results are conducive to a better understanding of the emergence of cooperation in the real world.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:973-983
    DOI: 10.1016/j.physa.2018.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118304217
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.04.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Jianlei & Zhang, Chunyan & Chu, Tianguang, 2011. "The evolution of cooperation in spatial groups," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 131-136.
    2. Keke Huang & Tao Wang & Yuan Cheng & Xiaoping Zheng, 2015. "Effect of Heterogeneous Investments on the Evolution of Cooperation in Spatial Public Goods Game," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-10, March.
    3. Cao, Xian-Bin & Du, Wen-Bo & Rong, Zhi-Hai, 2010. "The evolutionary public goods game on scale-free networks with heterogeneous investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(6), pages 1273-1280.
    4. Wang, Xianjia & Lv, Shaojie & Quan, Ji, 2017. "The evolution of cooperation in the Prisoner’s Dilemma and the Snowdrift game based on Particle Swarm Optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 286-295.
    5. 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.
    6. Li, Pei & Duan, Haibin, 2015. "Evolution of cooperation driven by incremental learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 14-22.
    7. Liu, Penghui & Liu, Jing, 2017. "Contribution diversity and incremental learning promote cooperation in public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 827-838.
    8. Francisco C. Santos & Marta D. Santos & Jorge M. Pacheco, 2008. "Social diversity promotes the emergence of cooperation in public goods games," Nature, Nature, vol. 454(7201), pages 213-216, July.
    9. Jianlei Zhang & Chunyan Zhang & Tianguang Chu & Matjaž Perc, 2011. "Resolution of the Stochastic Strategy Spatial Prisoner's Dilemma by Means of Particle Swarm Optimization," PLOS ONE, Public Library of Science, vol. 6(7), pages 1-7, July.
    10. 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.
    11. Urs Fischbacher & Simon Gachter, 2010. "Social Preferences, Beliefs, and the Dynamics of Free Riding in Public Goods Experiments," American Economic Review, American Economic Association, vol. 100(1), pages 541-556, March.
    12. Zhenhua Pei & Baokui Wang & Jinming Du, 2016. "Effects of income redistribution on the evolution of cooperation in spatial public goods games," Papers 1611.01531, arXiv.org.
    13. Wu, Te & Fu, Feng & Dou, Puxuan & Wang, Long, 2014. "Social influence promotes cooperation in the public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 86-93.
    14. Gao, Jia & Li, Zhi & Cong, Rui & Wang, Long, 2012. "Tolerance-based punishment in continuous public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4111-4120.
    15. Zhang, Haifeng & Yang, Hanxin & Du, Wenbo & Wang, Binghong & Cao, Xianbin, 2010. "Evolutionary public goods games on scale-free networks with unequal payoff allocation mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1099-1104.
    16. Li, Ming & Jia, Chun-Xiao & Liu, Run-Ran & Wang, Bing-Hong, 2013. "Emergence of cooperation in spatial public goods game with conditional participation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1840-1847.
    17. Cui, Guang-Hai & Li, Ming-Chu & Fan, Xin-Xin & Deonauth, Nakema & Wang, Zhen, 2014. "Optimism when winning and cautiousness when losing promote cooperation in the spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 181-189.
    18. Yang, Han-Xin & Rong, Zhihai & Lu, Pei-Min & Zeng, Yong-Zhi, 2012. "Effects of aspiration on public cooperation in structured populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(15), pages 4043-4049.
    19. Chen, Xiaojie & Fu, Feng & Wang, Long, 2008. "Promoting cooperation by local contribution under stochastic win-stay-lose-shift mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5609-5615.
    20. Wang, Yongjie & Chen, Tong & Chen, Qiao & Si, Guangrun, 2017. "Emotional decisions in structured populations for the evolution of public cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 475-481.
    21. Wang, Xiaofeng & Chen, Xiaojie & Gao, Jia & Wang, Long, 2013. "Reputation-based mutual selection rule promotes cooperation in spatial threshold public goods games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 181-187.
    22. Li, Zhi & Deng, Chuang & Suh, Il Hong, 2015. "Network topology control strategy based on spatial evolutionary public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 16-23.
    23. Fan, Ruguo & Zhang, Yingqing & Luo, Ming & Zhang, Hongjuan, 2017. "Promotion of cooperation induced by heterogeneity of both investment and payoff allocation in spatial public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 454-463.
    24. Li, Zhaofeng & Shen, Bi & Jiang, Yichuan, 2017. "The maintenance of cooperation in multiplex networks with limited and partible resources of agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 499-507.
    25. Kocher, Martin G. & Martinsson, Peter & Matzat, Dominik & Wollbrant, Conny, 2015. "The role of beliefs, trust, and risk in contributions to a public good," Journal of Economic Psychology, Elsevier, vol. 51(C), pages 236-244.
    26. Wang, Yongjie & Chen, Tong, 2015. "Heuristics guide cooperative behaviors in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 59-65.
    27. Shi, Dong-Mei & Wang, Bing-Hong, 2017. "Critical mass of public goods and its coevolution with cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 85-90.
    28. 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.
    29. Amado, André & Huang, Weini & Campos, Paulo R.A. & Ferreira, Fernando Fagundes, 2015. "Learning process in public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 21-31.
    30. Li, Yixiao & Shen, Bin, 2013. "The coevolution of partner switching and strategy updating in non-excludable public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4956-4965.
    31. Li, Yixiao & Jin, Xiaogang & Su, Xianchuang & Kong, Fansheng & Peng, Chengbin, 2010. "Cooperation and charity in spatial public goods game under different strategy update rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1090-1098.
    32. Wu-Jie Yuan & Cheng-Yi Xia, 2014. "Role of Investment Heterogeneity in the Cooperation on Spatial Public Goods Game," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-6, March.
    33. Yang, Han-Xin & Rong, Zhihai, 2015. "Mutual punishment promotes cooperation in the spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 230-234.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Huang, Xingjun & Lin, Yun & Lim, Ming K. & Zhou, Fuli & Liu, Feng, 2022. "Electric vehicle charging station diffusion: An agent-based evolutionary game model in complex networks," Energy, Elsevier, vol. 257(C).
    3. Altay, Elif Varol & Alatas, Bilal, 2020. "Randomness as source for inspiring solution search methods: Music based approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Quan, Ji & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Information fusion based on reputation and payoff promotes cooperation in spatial public goods game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    5. Tian, Yue & Gao, Shun & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2024. "Particle swarm intelligence promotes cooperation by adapting interaction radii in co-evolutionary games," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    6. Quan, Ji & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Evidential reasoning based on imitation and aspiration information in strategy learning promotes cooperation in optional spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Quan, Ji & Yang, Wenjun & Li, Xia & Wang, Xianjia & Yang, Jian-Bo, 2020. "Social exclusion with dynamic cost on the evolution of cooperation in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    8. Shuo Wang & Zhuang Li & Weidong Li & Hua Jiang, 2022. "Continuous Spatial Public Goods Game Based on Particle Swarm Optimization with Memory Stability," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    9. Zheng, Liping & Xu, Hedong & Tian, Cunzhi & Fan, Suohai, 2021. "Evolutionary dynamics of information in the market: Transmission and trust," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    10. Quan, Ji & Tang, Caixia & Wang, Xianjia, 2021. "Reputation-based discount effect in imitation on the evolution of cooperation in spatial public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    11. Lv, Shaojie & Song, Feifei, 2022. "Particle swarm intelligence and the evolution of cooperation in the spatial public goods game with punishment," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    12. Wang, Chaoqian & Huang, Chaochao, 2022. "Between local and global strategy updating in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    13. Ye, Wenxing & Fan, Suohai, 2020. "Evolutionary traveler’s dilemma game based on particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    14. Quan, Ji & Tang, Caixia & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Reputation evaluation with tolerance and reputation-dependent imitation on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    15. Zhao, Dan & Ji, Shou-feng & Wang, He-ping & Jiang, Li-wen, 2021. "How do government subsidies promote new energy vehicle diffusion in the complex network context? A three-stage evolutionary game model," Energy, Elsevier, vol. 230(C).
    16. Wang, Xianjia & Chen, Wenman, 2020. "Evolutionary dynamics in spatial threshold public goods game with the asymmetric return rate mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    17. Quan, Ji & Dong, Xu & Wang, Xianjia, 2022. "Rational conformity behavior in social learning promotes cooperation in spatial public goods game," Applied Mathematics and Computation, Elsevier, vol. 425(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Quan, Ji & Tang, Caixia & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Reputation evaluation with tolerance and reputation-dependent imitation on cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Shang, Lihui & Sun, Sihao & Ai, Jun & Su, Zhan, 2022. "Cooperation enhanced by the interaction diversity for the spatial public goods game on regular lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    3. Fan, Ruguo & Zhang, Yingqing & Luo, Ming & Zhang, Hongjuan, 2017. "Promotion of cooperation induced by heterogeneity of both investment and payoff allocation in spatial public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 454-463.
    4. Quan, Ji & Zhou, Yawen & Wang, Xianjia & Yang, Jian-Bo, 2020. "Information fusion based on reputation and payoff promotes cooperation in spatial public goods game," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    5. Quan, Ji & Tang, Caixia & Wang, Xianjia, 2021. "Reputation-based discount effect in imitation on the evolution of cooperation in spatial public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    6. Lu, Peng, 2015. "Individual choice and reputation distribution of cooperative behaviors among heterogeneous groups," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 39-46.
    7. Lu, Peng, 2015. "Imitating winner or sympathizing loser? Quadratic effects on cooperative behavior in prisoners’ dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 327-337.
    8. Wang, Hanchen & Sun, Yichun & Zheng, Lei & Du, Wenbo & Li, Yumeng, 2018. "The public goods game on scale-free networks with heterogeneous investment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 396-404.
    9. Chen, Qiao & Chen, Tong & Wang, Yongjie, 2017. "Publishing the donation list incompletely promotes the emergence of cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 48-56.
    10. Chuanyun Li & Xia Cao & Ming Chi, 2020. "Research on an evolutionary game model and simulation of a cluster innovation network based on fairness preference," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-17, January.
    11. Peng Lu & Xiaoping Zheng, 2015. "Social Stratification and Cooperative Behavior in Spatial Prisoners' Dilemma Games," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    12. Lu, Peng & Wang, Fang, 2015. "Heterogeneity of inferring reputation probability in cooperative behaviors for the spatial prisoners’ dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 367-378.
    13. Wang, Qun & Wang, Hanchen & Zhang, Zhuxi & Li, Yumeng & Liu, Yu & Perc, Matjaž, 2018. "Heterogeneous investments promote cooperation in evolutionary public goods games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 570-575.
    14. Lu, Peng, 2015. "Learn good from bad: Effects of good and bad neighbors in spatial prisoners’ dilemma games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 351-358.
    15. Quan, Ji & Liu, Wei & Chu, Yuqing & Wang, Xianjia, 2018. "Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 123-134.
    16. 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.
    17. Yu, Fengyuan & Wang, Jianwei & He, Jialu, 2022. "Inequal dependence on members stabilizes cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    18. Wang, Mie & Kang, HongWei & Shen, Yong & Sun, XingPing & Chen, QingYi, 2021. "The role of alliance cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Lee, Hsuan-Wei & Cleveland, Colin & Szolnoki, Attila, 2021. "Small fraction of selective cooperators can elevate general wellbeing significantly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    20. Zhenghong Wu & Huan Huang & Qinghu Liao, 2021. "The study on the role of dedicators on promoting cooperation in public goods game," PLOS ONE, Public Library of Science, vol. 16(9), pages 1-17, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:973-983. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.