IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v198y2025ics0960077925005296.html

The evolutionary fairness dynamics on multiplex networks with information reliability and time delays

Author

Listed:
  • Wang, Yang
  • Li, Xinlong
  • Yao, Jing
  • Zhang, Wei

Abstract

This paper studies the fairness behavior of an ultimatum game played on multiplex networks from the perspective of stability and consensus, which enables us to gain more insights into large-scale complex systems, ranging from biology to behavioral sciences to economics, regarding the evolution of fairness and cooperative behavior. In addition to existing works, a more realistic and challenging scenario is considered, where the credit and response capacity of each player are not assumed identical, and the possible distortion or delay in the information transmission is taken into account. The conditions for the system to asymptotically achieve fairness in two cases are rigorously derived which show an inversely proportional relationship between the largest eigenvalue of the normalized supra-Laplacian matrix and the critical offer division ratio, and reveal the effect of information reliability and time delay on the convergence property of the overall system. The results of theoretical analysis are verified via extensive numerical examples in which an indicator called the fairness index is used to measure the evolution of fairness.

Suggested Citation

  • Wang, Yang & Li, Xinlong & Yao, Jing & Zhang, Wei, 2025. "The evolutionary fairness dynamics on multiplex networks with information reliability and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005296
    DOI: 10.1016/j.chaos.2025.116516
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925005296
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116516?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Ling, Ting & Li, Zhang & Feng, Minyu & Szolnoki, Attila, 2025. "Supervised cooperation on interdependent public goods games," Applied Mathematics and Computation, Elsevier, vol. 492(C).
    2. Zhang, Yanling & Chen, Xiaojie & Liu, Aizhi & Sun, Changyin, 2018. "The effect of the stake size on the evolution of fairness," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 641-653.
    3. Allen, James M. & Hoyle, Rebecca B., 2017. "Asynchronous updates can promote the evolution of cooperation on multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 607-619.
    4. Feng, Kehuan & Han, Songlin & Feng, Minyu & Szolnoki, Attila, 2024. "An evolutionary game with reputation-based imitation-mutation dynamics," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    5. Yue, Hongyu & Xiong, Xiaojin & Feng, Minyu & Szolnoki, Attila, 2025. "Coevolution of relationship-driven cooperation under recommendation protocol on multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    6. Li, Gang & Sun, Xiaochen, 2021. "Evolutionary game on a growing multilayer network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    7. 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.
    8. Liu, Zhuo & Wang, Juan & Li, Xiaopeng, 2024. "Evolutionary dynamics of networked N-player trust games with exclusion strategy," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    9. Duan, Xiaofang & Ye, Jimin & Lu, Yikang & Du, Chunpeng & Jang, Bongsoo & Park, Junpyo, 2024. "Does cooperation among conspecifics facilitate the coexistence of species?," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    10. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    11. Amit Basak & Supratim Sengupta, 2024. "Evolution of cooperation in multichannel games on multiplex networks," PLOS Computational Biology, Public Library of Science, vol. 20(12), pages 1-26, December.
    12. Matteo Barigozzi & Giorgio Fagiolo & Diego Garlaschelli, 2009. "The Multi-Network of International Trade: A Commodity-Specific Analysis," LEM Papers Series 2009/09, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    13. M. N. Kuperman & S. Risau-Gusman, 2008. "The effect of the topology on the spatial ultimatum game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 62(2), pages 233-238, March.
    14. John M. McNamara & Zoltan Barta & Alasdair I. Houston, 2004. "Variation in behaviour promotes cooperation in the Prisoner's Dilemma game," Nature, Nature, vol. 428(6984), pages 745-748, April.
    15. Yanling Zhang & Jian Liu & Aming Li, 2019. "Effects of Empathy on the Evolutionary Dynamics of Fairness in Group-Structured Systems," Complexity, Hindawi, vol. 2019, pages 1-13, November.
    16. Zhao, Tingting & Hu, Cheng & Huang, Jie & Yu, Juan, 2024. "Fixed/Prescribed-time synchronization of multi-layer complex networks under switching control," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    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. Deng, Lili & Wang, Rugen & Liao, Ying & Xu, Ronghua & Wang, Cheng, 2025. "The reputation-based reward mechanism promotes the evolution of fairness," Applied Mathematics and Computation, Elsevier, vol. 486(C).
    2. Deng, Lili & Wang, Hongsi & Wang, Rugen & Xu, Ronghua & Wang, Cheng, 2024. "The adaptive adjustment of node weights based on reputation and memory promotes fairness," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Yanling Zhang & Jian Liu & Aming Li, 2019. "Effects of Empathy on the Evolutionary Dynamics of Fairness in Group-Structured Systems," Complexity, Hindawi, vol. 2019, pages 1-13, November.
    4. Zhao, Yakun & Xiong, Tianyu & Zheng, Lei & Li, Yumeng & Chen, Xiaojie, 2020. "The effect of similarity on the evolution of fairness in the ultimatum game," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Zhang, Yanling & Yang, Shuo & Chen, Xiaojie & Bai, Yanbing & Xie, Guangming, 2023. "Reputation update of responders efficiently promotes the evolution of fairness in the ultimatum game," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Jaime Iranzo & Luis M Floría & Yamir Moreno & Angel Sánchez, 2012. "Empathy Emerges Spontaneously in the Ultimatum Game: Small Groups and Networks," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-8, September.
    7. Li, Dandan & Wu, Qiongzi & Han, Dun, 2025. "On evolution of agent behavior under limited gaming time with reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    8. Deng, Lili & Li, Weiwei & Wang, Rugen & Wang, Cheng, 2025. "The impact of reputation-based dynamic reward mechanism on the evolution of fairness," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    9. Deng, Lili & Zhang, Xingxing & Wang, Cheng, 2021. "Coevolution of spatial ultimatum game and link weight promotes fairness," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    10. Xie, Kai & Liu, Yaojun & Liu, Tingjin, 2024. "Unveiling the masks: Deception and reputation in spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    11. Chen, Wei & Zhu, Qianlong & Wu, Te, 2023. "Unfairness promotes the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    12. Zheng, Lei & Li, Youqi & Zhou, Jingsai & Li, Yumeng, 2022. "The effect of celebrity on the evolution of fairness in the ultimatum game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    13. Deng, Lili & Tang, Wansheng & Zhang, Jianxiong, 2011. "The coevolutionary ultimatum game on different network topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4227-4235.
    14. Yue, Hongyu & Xiong, Xiaojin & Feng, Minyu & Szolnoki, Attila, 2025. "Dynamic evolution of cooperation based on adaptive reputation threshold and game transition," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    15. Perc, Matjaž & Grigolini, Paolo, 2013. "Collective behavior and evolutionary games – An introduction," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 1-5.
    16. Benko, Tina P. & Pi, Bin & Li, Qin & Feng, Minyu & Perc, Matjaž & Blažun Vošner, Helena, 2025. "Evolutionary games for cooperation in open data management," Applied Mathematics and Computation, Elsevier, vol. 496(C).
    17. Chen, Yunong & Belmonte, Andrew & Griffin, Christopher, 2021. "Imitation of success leads to cost of living mediated fairness in the Ultimatum Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    18. Rodrigo Mesa-Arango & Badri Narayanan & Satish V. Ukkusuri, 2019. "The Impact of International Crises on Maritime Transportation Based Global Value Chains," Networks and Spatial Economics, Springer, vol. 19(2), pages 381-408, June.
    19. Michael Seiler, 2014. "The Effect of Perceived Lender Characteristics and Market Conditions on Strategic Mortgage Defaults," The Journal of Real Estate Finance and Economics, Springer, vol. 48(2), pages 256-270, February.
    20. Robison, Lindon J. & Hanson, Steven D., 1995. "Social Capital and Economic Cooperation," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 27(1), pages 43-58, July.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:eee:chsofr:v:198:y:2025:i:c:s0960077925005296. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.