IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v375y2020ics0096300320300461.html
   My bibliography  Save this article

Diffusion sustains cooperation via forming diverse spatial patterns in prisoner's dilemma game

Author

Listed:
  • Liu, Yan-Ping
  • Wang, Lin
  • Zhang, Feng
  • Wang, Rui-Wu

Abstract

How cooperation arouses and maintains in social dilemmas has long been the core problem in evolutionary biology. Assortative interaction has been identified as a fundamental mechanism for cooperation in the social dilemma games. Many studies have shown that spatial limitation can lead to cooperation evolution, but how spatial pattern shape the cooperation is studied rarely. In this paper, using a spatial model of eco-evolutionary prisoner's dilemma game, where the player's diffusion is incorporated definitely, we show that the diffusion can trigger out rich spatial patterns. These self-organized spatial patterns could profoundly affect the cooperation level and system stability. Totally, six types of patterns can be identified according to their influences on cooperation evolution. Cooperation is affected by the spatial configuration of population distributions: spot- or stripe- type pattern promotes the cooperation, but mixed form of them or spatial synchrony suppresses cooperation. In contrast, uniform pattern has no effect on cooperation. Meanwhile, the analysis of spatial autocorrelation about population distributions via local Moran index reveals that the difference of spatial correlations among adjacent sites may be responsible for the functional differentiation of such self-organized structures. Spatial diffusion arouses vastly different spatial patterns, which renders the spatial extension system greatly expands the survival region of cooperators, i.e., the game dynamics continues after the homogeneous system has collapsed. Those results are helpful to understand the function of spatial patterns in supporting cooperation and fostering behavioral diversity.

Suggested Citation

  • Liu, Yan-Ping & Wang, Lin & Zhang, Feng & Wang, Rui-Wu, 2020. "Diffusion sustains cooperation via forming diverse spatial patterns in prisoner's dilemma game," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300461
    DOI: 10.1016/j.amc.2020.125077
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320300461
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125077?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. Tanimoto, Jun, 2010. "The effect of assortativity by degree on emerging cooperation in a 2×2 dilemma game played on an evolutionary network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3325-3335.
    2. Bo, Xianyu, 2010. "Other-regarding preference and the evolutionary prisoner’s dilemma on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1105-1114.
    3. Paul B. Rainey & Katrina Rainey, 2003. "Evolution of cooperation and conflict in experimental bacterial populations," Nature, Nature, vol. 425(6953), pages 72-74, September.
    4. Avner Shaked & Ilan Eshel & Emilia Sansone, 1999. "The emergence of kinship behavior in structured populations of unrelated individuals," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 447-463.
    5. Yanguang Chen, 2013. "New Approaches for Calculating Moran’s Index of Spatial Autocorrelation," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    6. Erte Xiao & Howard Kunreuther, 2016. "Punishment and Cooperation in Stochastic Social Dilemmas," Journal of Conflict Resolution, Peace Science Society (International), vol. 60(4), pages 670-693, June.
    7. 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.
    8. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    9. Ernst Fehr & Urs Fischbacher, 2003. "The nature of human altruism," Nature, Nature, vol. 425(6960), pages 785-791, October.
    10. Feng Zhang & Cang Hui, 2011. "Eco-Evolutionary Feedback and the Invasion of Cooperation in Prisoner's Dilemma Games," PLOS ONE, Public Library of Science, vol. 6(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. Zhao, Shanshan & Pan, Qiuhui & Zhu, Wenqiang & He, Mingfeng, 2023. "How “punishing evil and promoting good” promotes cooperation in social dilemma," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    2. Bartoš, Vojtěch, 2021. "Seasonal scarcity and sharing norms," Journal of Economic Behavior & Organization, Elsevier, vol. 185(C), pages 303-316.
    3. Zhao, Zhengwu & Zhang, Chunyan, 2023. "The mechanisms of labor division from the perspective of task urgency and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    4. Boyer, Tristan & Jonard, Nicolas, 2014. "Imitation and efficient contagion," Journal of Economic Behavior & Organization, Elsevier, vol. 100(C), pages 20-32.
    5. van den Bergh, Jeroen C.J.M. & Gowdy, John M., 2009. "A group selection perspective on economic behavior, institutions and organizations," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 1-20, October.
    6. Hirofumi Takesue, 2020. "From defection to ingroup favoritism to cooperation: simulation analysis of the social dilemma in dynamic networks," Journal of Computational Social Science, Springer, vol. 3(1), pages 189-207, April.
    7. Jason A Aimone & Daniel Houser, 2011. "Beneficial Betrayal Aversion," PLOS ONE, Public Library of Science, vol. 6(3), pages 1-5, March.
    8. Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    9. Yali Dong & Cong Li & Yi Tao & Boyu Zhang, 2015. "Evolution of Conformity in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-12, September.
    10. Zhang, Wei, 2024. "Network reciprocity and inequality: The role of additional mixing links among social groups," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    11. Li, Yixiao & Wang, Yi & Sheng, Jichuan, 2017. "The evolution of cooperation on geographical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 1-10.
    12. Anne-Ly Do & Lars Rudolf & Thilo Gross, 2012. "Coordination, Differentiation and Fairness in a Population of Cooperating Agents," Games, MDPI, vol. 3(1), pages 1-11, March.
    13. Ismael T Freire & Clement Moulin-Frier & Marti Sanchez-Fibla & Xerxes D Arsiwalla & Paul F M J Verschure, 2020. "Modeling the formation of social conventions from embodied real-time interactions," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-22, June.
    14. Xiaofeng Wang & Xiaojie Chen & Long Wang, 2020. "Evolution of egalitarian social norm by resource management," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-16, January.
    15. Hannes Rusch, 2013. "What niche did human cooperativeness evolve in?," MAGKS Papers on Economics 201327, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    16. 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.
    17. repec:ipg:wpaper:2014-052 is not listed on IDEAS
    18. Tanimoto, Jun, 2013. "Coevolutionary, coexisting learning and teaching agents model for prisoner’s dilemma games enhancing cooperation with assortative heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2955-2964.
    19. Jianguo Ren & Yonghong Xu, 2014. "Modelling the Effects of Selection Temperature and Mutation on the Prisoner’s Dilemma Game on a Complete Oriented Star," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-9, October.
    20. Li, Guangyu & Du, Haifeng & He, Xiaochen, 2024. "The evolutionary prisoner’s dilemma game in continuous signed networks," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    21. Guangming Ren & Lan Liu & Mingku Feng & Yingji He, 2018. "Coevolution of public goods game and networks based on survival of the fittest," PLOS ONE, Public Library of Science, vol. 13(9), pages 1-11, 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:apmaco:v:375:y:2020:i:c:s0096300320300461. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.