IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0021787.html
   My bibliography  Save this article

Resolution of the Stochastic Strategy Spatial Prisoner's Dilemma by Means of Particle Swarm Optimization

Author

Listed:
  • Jianlei Zhang
  • Chunyan Zhang
  • Tianguang Chu
  • Matjaž Perc

Abstract

We study the evolution of cooperation among selfish individuals in the stochastic strategy spatial prisoner's dilemma game. We equip players with the particle swarm optimization technique, and find that it may lead to highly cooperative states even if the temptations to defect are strong. The concept of particle swarm optimization was originally introduced within a simple model of social dynamics that can describe the formation of a swarm, i.e., analogous to a swarm of bees searching for a food source. Essentially, particle swarm optimization foresees changes in the velocity profile of each player, such that the best locations are targeted and eventually occupied. In our case, each player keeps track of the highest payoff attained within a local topological neighborhood and its individual highest payoff. Thus, players make use of their own memory that keeps score of the most profitable strategy in previous actions, as well as use of the knowledge gained by the swarm as a whole, to find the best available strategy for themselves and the society. Following extensive simulations of this setup, we find a significant increase in the level of cooperation for a wide range of parameters, and also a full resolution of the prisoner's dilemma. We also demonstrate extreme efficiency of the optimization algorithm when dealing with environments that strongly favor the proliferation of defection, which in turn suggests that swarming could be an important phenomenon by means of which cooperation can be sustained even under highly unfavorable conditions. We thus present an alternative way of understanding the evolution of cooperative behavior and its ubiquitous presence in nature, and we hope that this study will be inspirational for future efforts aimed in this direction.

Suggested Citation

  • 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.
  • Handle: RePEc:plo:pone00:0021787
    DOI: 10.1371/journal.pone.0021787
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0021787
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0021787&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0021787?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
    ---><---

    References listed on IDEAS

    as
    1. Bin Wu & Da Zhou & Feng Fu & Qingjun Luo & Long Wang & Arne Traulsen, 2010. "Evolution of Cooperation on Stochastic Dynamical Networks," PLOS ONE, Public Library of Science, vol. 5(6), pages 1-7, June.
    2. Marco Tomassini & Enea Pestelacci & Leslie Luthi, 2007. "Social Dilemmas And Cooperation In Complex Networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1173-1185.
    3. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    4. M. Droz & J. Szwabiński & G. Szabó, 2009. "Motion of influential players can support cooperation in Prisoner’s Dilemma," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 579-585, October.
    5. Julia Poncela & Jesús Gómez-Gardeñes & Luis M Floría & Angel Sánchez & Yamir Moreno, 2008. "Complex Cooperative Networks from Evolutionary Preferential Attachment," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-6, June.
    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. 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.
    3. Jun, Luo & Liheng, Liu & Xianyi, Wu, 2015. "A double-subpopulation variant of the bat algorithm," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 361-377.
    4. 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.
    5. García Nieto, P.J. & García-Gonzalo, E. & Sánchez Lasheras, F. & de Cos Juez, F.J., 2015. "Hybrid PSO–SVM-based method for forecasting of the remaining useful life for aircraft engines and evaluation of its reliability," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 219-231.
    6. 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).
    7. Wang, Jianwei & Xu, Wenshu & Zhang, Xingjian & Zhao, Nianxuan & Yu, Fengyuan, 2023. "Redistribution based on willingness to cooperate promotes cooperation while intensifying equality in heterogeneous populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    8. Bahbouhi, Jalal Eddine & Elkouay, Abdelali & Bouderba, Saif Islam & Moussa, Najem, 2024. "The whale optimization algorithm and the evolution of cooperation in the spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. 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).
    10. 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).
    11. 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).
    12. Chen, Ya-Shan & Yang, Han-Xin & Guo, Wen-Zhong & Liu, Geng-Geng, 2018. "Promotion of cooperation based on swarm intelligence in spatial public goods games," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 614-620.
    13. Zhang, Chunyan & Zhang, Jianlei & Xie, Guangming, 2014. "Evolution of cooperation among game players with non-uniform migration scopes," Chaos, Solitons & Fractals, Elsevier, vol. 59(C), pages 103-111.
    14. Li, Jiaqi & Zhang, Chunyan & Sun, Qinglin & Chen, Zengqiang, 2015. "Coevolution between strategy and social networks structure promotes cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 253-263.
    15. Guanming Cheng & Lei Wang & Ryan Loxton & Qun Lin, 2015. "Robust Optimal Control of a Microbial Batch Culture Process," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 342-362, October.
    16. 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.

    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. 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. 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.
    3. Te Wu & Feng Fu & Long Wang, 2011. "Moving Away from Nasty Encounters Enhances Cooperation in Ecological Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-7, November.
    4. Jorge Peña & Yannick Rochat, 2012. "Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-13, September.
    5. 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).
    6. Michael Foley & Rory Smead & Patrick Forber & Christoph Riedl, 2021. "Avoiding the bullies: The resilience of cooperation among unequals," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-18, April.
    7. 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.
    8. Wang, Zhen & Chen, Tong & Wang, Yongjie, 2017. "Leadership by example promotes the emergence of cooperation in public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 100-105.
    9. Scatà, Marialisa & Di Stefano, Alessandro & La Corte, Aurelio & Liò, Pietro & Catania, Emanuele & Guardo, Ermanno & Pagano, Salvatore, 2016. "Combining evolutionary game theory and network theory to analyze human cooperation patterns," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 17-24.
    10. Luciano Miranda & Adauto J F de Souza & Fernando F Ferreira & Paulo R A Campos, 2012. "Complex Transition to Cooperative Behavior in a Structured Population Model," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-9, June.
    11. 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.
    12. Liu, Penghui & Liu, Jing, 2017. "Robustness of coevolution in resolving prisoner’s dilemma games on interdependent networks subject to attack," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 362-370.
    13. Shijun Wang & Máté S Szalay & Changshui Zhang & Peter Csermely, 2008. "Learning and Innovative Elements of Strategy Adoption Rules Expand Cooperative Network Topologies," PLOS ONE, Public Library of Science, vol. 3(4), pages 1-9, April.
    14. Matjaž Perc & Zhen Wang, 2010. "Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-8, December.
    15. Cheng-Yi Xia & Xiao-Kun Meng & Zhen Wang, 2015. "Heterogeneous Coupling between Interdependent Lattices Promotes the Cooperation in the Prisoner’s Dilemma Game," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-13, June.
    16. Zhang, Xin-Jie & Tang, Yong & Xiong, Jason & Wang, Wei-Jia & Zhang, Yi-Cheng, 2020. "Ranking game on networks: The evolution of hierarchical society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    17. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    18. Wes Maciejewski & Feng Fu & Christoph Hauert, 2014. "Evolutionary Game Dynamics in Populations with Heterogenous Structures," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-16, April.
    19. Kokubo, Satoshi & Wang, Zhen & Tanimoto, Jun, 2015. "Spatial reciprocity for discrete, continuous and mixed strategy setups," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 552-568.
    20. Chica, Manuel & Santos, Francisco C., 2023. "Seeding leading cooperators and institutions in networked climate dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0021787. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.