IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v12y2022i4d10.1007_s13235-022-00443-1.html
   My bibliography  Save this article

Evolutionary Game Dynamics in a Finite Continental Island Population Model and Emergence of Cooperation

Author

Listed:
  • Véronique Ladret

    (Université de Montpellier)

Abstract

We consider the continental island model for a finite haploid population with a total number of $${\textit{n}}$$ n demes consisting of one continent and $$n-1$$ n - 1 islands. We assume viability differences in the population captured by a linear game within each deme as a result of pairwise interactions. Assuming weak selection, conservative migration and the limit case of the structured coalescent assumptions, we derive the first-order approximation for the fixation probability of a single mutant, initially introduced in the continent, with respect to the intensity of selection. This result is applied to the case of the iterated Prisoner’s Dilemma, when the resident strategy is always defect and the mutant cooperative strategy is tit-for-tat. In this context, we investigate the condition under which selection favors the emergence of cooperation and we derive an extension of the “one-third law” of evolution. When the continent and the islands are of the same size, we compare the continental island model to its Wright’s island model counterpart. When the islands have the same size, but this size differs from the size of the continent, we investigate how the asymmetry in the deme sizes can better promote the evolution of tit-for-tat compared to its equal deme sizes model counterpart.

Suggested Citation

  • Véronique Ladret, 2022. "Evolutionary Game Dynamics in a Finite Continental Island Population Model and Emergence of Cooperation," Dynamic Games and Applications, Springer, vol. 12(4), pages 1338-1375, December.
  • Handle: RePEc:spr:dyngam:v:12:y:2022:i:4:d:10.1007_s13235-022-00443-1
    DOI: 10.1007/s13235-022-00443-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-022-00443-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13235-022-00443-1?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. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    2. 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.
    3. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    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. Benjamin Allen & Christine Sample & Robert Jencks & James Withers & Patricia Steinhagen & Lori Brizuela & Joshua Kolodny & Darren Parke & Gabor Lippner & Yulia A Dementieva, 2020. "Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-20, January.
    2. McAvoy, Alex & Fraiman, Nicolas & Hauert, Christoph & Wakeley, John & Nowak, Martin A., 2018. "Public goods games in populations with fluctuating size," Theoretical Population Biology, Elsevier, vol. 121(C), pages 72-84.
    3. Liu, Xuesong & Pan, Qiuhui & He, Mingfeng & Liu, Aizhi, 2019. "Promotion of cooperation in evolutionary game dynamics under asymmetric information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 258-266.
    4. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    5. Li, Bin-Quan & Wu, Zhi-Xi & Guan, Jian-Yue, 2022. "Critical thresholds of benefit distribution in an extended snowdrift game model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. 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.
    7. Wang, Chaoqian & Szolnoki, Attila, 2023. "Inertia in spatial public goods games under weak selection," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    8. Xiaochen Wang & Lei Zhou & Alex McAvoy & Aming Li, 2023. "Imitation dynamics on networks with incomplete information," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    9. Wang, Jianwei & Xu, Wenshu & Chen, Wei & Yu, Fengyuan & He, Jialu, 2021. "Inter-group selection of strategy promotes cooperation in public goods game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    10. Simon D Angus & Jonathan Newton, 2020. "Collaboration leads to cooperation on sparse networks," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-11, January.
    11. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    12. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    13. Alex McAvoy & Andrew Rao & Christoph Hauert, 2021. "Intriguing effects of selection intensity on the evolution of prosocial behaviors," PLOS Computational Biology, Public Library of Science, vol. 17(11), pages 1-21, November.
    14. 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.
    15. Lv, Shaojie & Zhao, Changheng & Li, Jiaying, 2022. "Generosity in public goods game with the aspiration-driven rule," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    16. M. Kleshnina & K. Kaveh & K. Chatterjee, 2020. "The role of behavioural plasticity in finite vs infinite populations," Papers 2009.13160, arXiv.org.
    17. Peng Liu & Haoxiang Xia, 2015. "Structure and evolution of co-authorship network in an interdisciplinary research field," Scientometrics, Springer;Akadémiai Kiadó, vol. 103(1), pages 101-134, April.
    18. 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.
    19. 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).
    20. Lessard, Sabin & Lahaie, Philippe, 2009. "Fixation probability with multiple alleles and projected average allelic effect on selection," Theoretical Population Biology, Elsevier, vol. 75(4), pages 266-277.

    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:spr:dyngam:v:12:y:2022:i:4:d:10.1007_s13235-022-00443-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.