IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v655y2024ics0378437124006939.html
   My bibliography  Save this article

Social dilemmas, network reciprocity, and small-world property

Author

Listed:
  • Pereira, F.B.
  • Ferreira, R.S.
  • Alencar, D.S.M.
  • Alves, T.F.A.
  • Alves, G.A.
  • Lima, F.W.S.
  • Macedo-Filho, A.

Abstract

We revisit two evolutionary game theory models, namely the Prisoner and the Snowdrift dilemmas, on top of small-world networks. These dynamics on networked populations (individuals occupying nodes of a graph) are mainly concerned with the competition between cooperating or defecting by allowing some process of revision of strategies. Cooperators avoid defectors by forming clusters in a process known as network reciprocity. This defense strategy is based on the fact that any individual interacts only with its nearest neighbors. The minimum cluster, in turn, is formed by a set of three completely connected nodes, and the bulk of these triplets is associated with the transitivity property of a network. We show that the transitivity increases eventually, assuming a constant behavior when observed as a function of the number of contacts an individual has. We investigate the influence of the network reciprocity on that transitivity-increasing regime on promoting cooperative behavior. The dynamics of small-world networks are compared with those of random regular and annealed networks, the latter typically studied as the well-mixed approach. The Snowdrift Game converges to an annealed scenario as randomness and coordination numbers increase. In contrast, the Prisoner’s Dilemma becomes more severe against the cooperative behavior under an increasing network reciprocity regime.

Suggested Citation

  • Pereira, F.B. & Ferreira, R.S. & Alencar, D.S.M. & Alves, T.F.A. & Alves, G.A. & Lima, F.W.S. & Macedo-Filho, A., 2024. "Social dilemmas, network reciprocity, and small-world property," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 655(C).
  • Handle: RePEc:eee:phsmap:v:655:y:2024:i:c:s0378437124006939
    DOI: 10.1016/j.physa.2024.130184
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437124006939
    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.2024.130184?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. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
    2. R. Luce & Albert Perry, 1949. "A method of matrix analysis of group structure," Psychometrika, Springer;The Psychometric Society, vol. 14(2), pages 95-116, June.
    3. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    4. 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.
    5. Jia, Chun-Xiao & Ma, Lin & Liu, Run-Ran, 2024. "Enhancing cooperation through payoff-related inertia in networked prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    6. Paul E. Turner & Lin Chao, 1999. "Prisoner's dilemma in an RNA virus," Nature, Nature, vol. 398(6726), pages 441-443, April.
    7. Ronan Ferreira & Silvio Ferreira, 2013. "Critical behavior of the contact process on small-world networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(11), pages 1-7, November.
    Full references (including those not matched with items on IDEAS)

    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. Qinghu Liao & Wenwen Dong & Boxin Zhao, 2023. "A New Strategy to Solve “the Tragedy of the Commons” in Sustainable Grassland Ecological Compensation: Experience from Inner Mongolia, China," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    2. Zhang, Lan & Huang, Changwei, 2023. "Preferential selection to promote cooperation on degree–degree correlation networks in spatial snowdrift games," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    3. Lefeng Cheng & Pan Peng & Wentian Lu & Pengrong Huang & Yang Chen, 2024. "Study of Flexibility Transformation in Thermal Power Enterprises under Multi-Factor Drivers: Application of Complex-Network Evolutionary Game Theory," Mathematics, MDPI, vol. 12(16), pages 1-23, August.
    4. Yunsheng Deng & Jihui Zhang, 2022. "The choice-decision based on memory and payoff favors cooperation in stag hunt game on interdependent networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-13, February.
    5. Theodore Tsekeris, 2025. "Transformations in the European Gas Supply Network Due to the Russia–Ukraine Conflict," Energies, MDPI, vol. 18(7), pages 1-21, March.
    6. Yang, Xiaomeng & Kong, Lingkai & Qu, Sen, 2024. "Evolution of technology cooperation networks based on networked evolutionary games model: An industrial heterogeneity perspective," Technology in Society, Elsevier, vol. 78(C).
    7. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    8. Yao Meng & Sean P. Cornelius & Yang-Yu Liu & Aming Li, 2024. "Dynamics of collective cooperation under personalised strategy updates," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    9. Takahara, Akihiro & Sakiyama, Tomoko, 2023. "Twisted strategy may enhance the evolution of cooperation in spatial prisoner’s dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    10. Samrachana Adhikari & Beau Dabbs, 2018. "Social Network Analysis in R: A Software Review," Journal of Educational and Behavioral Statistics, , vol. 43(2), pages 225-253, April.
    11. Wang, Xiaojie & Slamu, Wushour & Guo, Wenqiang & Wang, Sixiu & Ren, Yan, 2022. "A novel semi local measure of identifying influential nodes in complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    12. 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.
    13. Konstantinos Antoniadis & Kostas Zafiropoulos & Vasiliki Vrana, 2016. "A Method for Assessing the Performance of e-Government Twitter Accounts," Future Internet, MDPI, vol. 8(2), pages 1-18, April.
    14. Lin, Dan & Wu, Jiajing & Xuan, Qi & Tse, Chi K., 2022. "Ethereum transaction tracking: Inferring evolution of transaction networks via link prediction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    15. Ferreira, D.S.R. & Ribeiro, J. & Oliveira, P.S.L. & Pimenta, A.R. & Freitas, R.P. & Dutra, R.S. & Papa, A.R.R. & Mendes, J.F.F., 2022. "Spatiotemporal analysis of earthquake occurrence in synthetic and worldwide data," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    16. 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.
    17. Yue Chen & Xiaojian Niu & Yan Zhang, 2019. "Exploring Contrarian Degree in the Trading Behavior of China's Stock Market," Complexity, Hindawi, vol. 2019, pages 1-12, April.
    18. Noah E. Friedkin, 1984. "Structural Cohesion and Equivalence Explanations of Social Homogeneity," Sociological Methods & Research, , vol. 12(3), pages 235-261, February.
    19. Lv, Shaojie & Wang, Xianjia, 2020. "The impact of heterogeneous investments on the evolution of cooperation in public goods game with exclusion," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    20. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.

    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:655:y:2024:i:c:s0378437124006939. 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.