IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v10y2018i1p1-d192422.html
   My bibliography  Save this article

Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out

Author

Listed:
  • Alexander G. Ginsberg

    (Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
    Current address: Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA)

  • Feng Fu

    (Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA
    Department of Biomedical Data Science, Geisel School of Medicine at Dartmouth, Lebanon, NH 03756, USA)

Abstract

We study the evolution of cooperation in group interactions where players are randomly drawn from well-mixed populations of finite size to participate in a public goods game. However, due to the possibility of unforeseen circumstances, each player has a fixed probability of being unable to participate in the game, unlike previous models which assume voluntary participation. We first study how prescribed stochastic opting-out affects cooperation in finite populations, and then generalize for the limiting case of large populations. Because we use a pairwise comparison updating rule, our results apply to both genetic and behavioral evolution mechanisms. Moreover, in the model, cooperation is favored by natural selection over both neutral drift and defection if the return on investment exceeds a threshold value depending on the population size, the game size, and a player’s probability of opting-out. Our analysis further shows that, due to the stochastic nature of the opting-out in finite populations, the threshold of return on investment needed for natural selection to favor cooperation is actually greater than the one corresponding to compulsory games with the equal expected game size. We also use adaptive dynamics to study the co-evolution of cooperation and opting-out behavior. Indeed, given rare mutations minutely different from the resident population, an analysis based on adaptive dynamics suggests that over time the population will tend towards complete defection and non-participation, and subsequently cooperators abstaining from the public goods game will stand a chance to emerge by neutral drift, thereby paving the way for the rise of participating cooperators. Nevertheless, increasing the probability of non-participation decreases the rate at which the population tends towards defection when participating. Our work sheds light on understanding how stochastic opting-out emerges in the first place and on its role in the evolution of cooperation.

Suggested Citation

  • Alexander G. Ginsberg & Feng Fu, 2018. "Evolution of Cooperation in Public Goods Games with Stochastic Opting-Out," Games, MDPI, vol. 10(1), pages 1-27, December.
  • Handle: RePEc:gam:jgames:v:10:y:2018:i:1:p:1-:d:192422
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/10/1/1/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2073-4336/10/1/1/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Faqi Du & Feng Fu, 2011. "Partner Selection Shapes the Strategic and Topological Evolution of Cooperation," Dynamic Games and Applications, Springer, vol. 1(3), pages 354-369, September.
    2. Marco Alberto Javarone, 2016. "Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-6, February.
    3. Te Wu & Feng Fu & Yanling Zhang & Long Wang, 2013. "The Increased Risk of Joint Venture Promotes Social Cooperation," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-10, June.
    4. 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.
    5. R. Mark Isaac & James M. Walker, 1988. "Group Size Effects in Public Goods Provision: The Voluntary Contributions Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 179-199.
    6. 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.
    7. Marco Alberto Javarone & Daniele Marinazzo, 2017. "Evolutionary dynamics of group formation," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-10, November.
    8. Marco Alberto Javarone, 2016. "Statistical physics of the spatial Prisoner’s Dilemma with memory-aware agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-6, February.
    9. Jorge M Pacheco & Vítor V Vasconcelos & Francisco C Santos & Brian Skyrms, 2015. "Co-evolutionary Dynamics of Collective Action with Signaling for a Quorum," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-12, February.
    10. 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.
    11. Karl Sigmund & Hannelore De Silva & Arne Traulsen & Christoph Hauert, 2010. "Social learning promotes institutions for governing the commons," Nature, Nature, vol. 466(7308), pages 861-863, August.
    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. Xiaofeng Wang, 2021. "Costly Participation and The Evolution of Cooperation in the Repeated Public Goods Game," Dynamic Games and Applications, Springer, vol. 11(1), pages 161-183, March.
    2. Zhong, Li-Xin & Xu, Wen-Juan & Chen, Rong-Da & He, Yun-Xin & Qiu, Tian & Ren, Fei & Shi, Yong-Dong & Zhong, Chen-Yang, 2020. "Multiple learning mechanisms promote cooperation in public goods games with project selection," Chaos, Solitons & Fractals, Elsevier, vol. 133(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. de Oliveira, B.F. & de Moraes, M.V. & Bazeia, D. & Szolnoki, A., 2021. "Mobility driven coexistence of living organisms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    2. Cheng, Jiangjiang & Mei, Wenjun & Su, Wei & Chen, Ge, 2023. "Evolutionary games on networks: Phase transition, quasi-equilibrium, and mathematical principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    3. Christian Hilbe & Maria Kleshnina & Kateřina Staňková, 2023. "Evolutionary Games and Applications: Fifty Years of ‘The Logic of Animal Conflict’," Dynamic Games and Applications, Springer, vol. 13(4), pages 1035-1048, December.
    4. 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).
    5. Zhang, Liming & Li, Haihong & Dai, Qionglin & Yang, Junzhong, 2022. "Migration based on environment comparison promotes cooperation in evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    6. Javarone, Marco Alberto, 2016. "An evolutionary strategy based on partial imitation for solving optimization problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 262-269.
    7. 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.
    8. Wang, Jianwei & Xu, Wenshu & Yu, Fengyuan & He, Jialu & Chen, Wei & Dai, Wenhui, 2024. "Evolution of cooperation under corrupt institutions," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    9. Wang, Xiaofeng & Perc, Matjaž, 2021. "Emergence of cooperation in spatial social dilemmas with expulsion," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    10. Fang, Yinhai & Xu, Haiyan & Perc, Matjaž & Tan, Qingmei, 2019. "Dynamic evolution of economic networks under the influence of mergers and divestitures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 89-99.
    11. Chen, Wei & Zhu, Qianlong & Wu, Te, 2023. "Unfairness promotes the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    12. Chen, Wei & Wang, Jianwei & Yu, Fengyuan & He, Jialu & Xu, Wenshu & Wang, Rong, 2021. "Effects of emotion on the evolution of cooperation in a spatial prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    13. Wang, Shengxian & Chen, Xiaojie & Xiao, Zhilong & Szolnoki, Attila, 2022. "Decentralized incentives for general well-being in networked public goods game," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    14. Shu, Feng & Liu, Yaojun & Liu, Xingwen & Zhou, Xiaobing, 2019. "Memory-based conformity enhances cooperation in social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 480-490.
    15. 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).
    16. 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.
    17. Ji, Jiezhou & Pan, Qiuhui & Zhu, Wenqiang & He, Mingfeng, 2023. "The influence of own historical information and environmental historical information on the evolution of cooperation," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    18. Mark Broom & Igor V. Erovenko & Jan Rychtář, 2021. "Modelling Evolution in Structured Populations Involving Multiplayer Interactions," Dynamic Games and Applications, Springer, vol. 11(2), pages 270-293, June.
    19. Mo, Fei & Han, Wenchen, 2024. "Long homogeneous payoff records with the latest strategy promotes the cooperation," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    20. José M Galán & Maciej M Łatek & Seyed M Mussavi Rizi, 2011. "Axelrod's Metanorm Games on Networks," PLOS ONE, Public Library of Science, vol. 6(5), pages 1-11, May.

    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:gam:jgames:v:10:y:2018:i:1:p:1-:d:192422. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.