IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v501y2025ics0096300325001961.html

Group size dynamics for a group following game with shared rewards

Author

Listed:
  • Wettergren, Thomas A.

Abstract

We consider a population game in which a group of mobile individuals must repeatedly decide between two strategies: following other neighbors or moving on their own. When following others there is an improvement due to directed motion but a sharing of the credit for any rewards obtained. Conversely, the individual strategy provides for a full share of the credit for any rewards obtained at the cost of less-directed motion. This process leads to a dilemma with dynamically adjusting strategies and a resulting dynamic change in the number of group followers. The process is modeled as an evolutionary game with simple parameters that describe the differences in the motion opportunities and the sharing of rewards. A detailed analysis of the dynamics of the game is presented to show how the parameters affect the resulting equilibria solutions. Numerical methods are used to validate the analysis conclusions and simulations are performed to validate the analytical model of the evolutionary game.

Suggested Citation

  • Wettergren, Thomas A., 2025. "Group size dynamics for a group following game with shared rewards," Applied Mathematics and Computation, Elsevier, vol. 501(C).
    • Handle: RePEc:eee:apmaco:v:501:y:2025:i:c:s0096300325001961
    DOI: 10.1016/j.amc.2025.129470
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325001961
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129470?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. Wettergren, Thomas A., 2021. "Game-based modeling of independent searchers who share a common goal," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    2. Gary Charness & Luca Rigotti & Aldo Rustichini, 2007. "Individual Behavior and Group Membership," American Economic Review, American Economic Association, vol. 97(4), pages 1340-1352, September.
    3. You, Feng & Yang, Han-Xin & Li, Yumeng & Du, Wenbo & Wang, Gang, 2023. "A modified Vicsek model based on the evolutionary game," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    4. Tobias Reichenbach & Mauro Mobilia & Erwin Frey, 2007. "Mobility promotes and jeopardizes biodiversity in rock–paper–scissors games," Nature, Nature, vol. 448(7157), pages 1046-1049, August.
    5. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    6. Michael Richter & Ariel Rubinstein, 2021. "Holding a Group Together: Non-Game Theory Versus Game Theory," The Economic Journal, Royal Economic Society, vol. 131(638), pages 2629-2641.
    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. 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.
    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. Fulin Guo, 2023. "Experience-weighted attraction learning in network coordination games," Papers 2310.18835, arXiv.org.
    2. Zha, Jiajing & Li, Cong & Fan, Suohai, 2022. "The effect of stability-based strategy updating on cooperation in evolutionary social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    3. Ding, Zhen-Wei & Zhang, Ji-Qiang & Zheng, Guo-Zhong & Cai, Wei-Ran & Cai, Chao-Ran & Chen, Li & Wang, Xu-Ming, 2024. "Emergence of anti-coordinated patterns in snowdrift game by reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    4. Hu, Xiang & Liu, Xingwen & Zhou, Xiaobing, 2022. "A proportional-neighborhood-diversity evolution in snowdrift game on square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    5. Sarkar, Bijan, 2021. "The cooperation–defection evolution on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    6. Shu, Feng & Liu, Xingwen & Fang, Kai & Chen, Hao, 2018. "Memory-based snowdrift game on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 15-26.
    7. Zhang, Jing & Li, Zhao & Zhang, Jiqiang & Ma, Lin & Zheng, Guozhong & Chen, Li, 2023. "Emergence of oscillatory cooperation in a population with incomplete information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    8. Zhang, Jun & Hu, Bin & Huang, Yi Jie & Deng, Zheng Hong & Wu, Tao, 2020. "The evolution of cooperation affected by aspiration-driven updating rule in multi-games with voluntary participation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. Du, Faqi & Fu, Feng, 2013. "Quantifying the impact of noise on macroscopic organization of cooperation in spatial games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 35-44.
    10. Huang, Yijie & Chen, Yanhong, 2025. "Multi-games on a dynamic network and the evolution of cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    11. Huang, Yi Jie & Deng, Zheng Hong & Song, Qun & Wu, Tao & Deng, Zhi Long & Gao, Ming yu, 2019. "The evolution of cooperation in multi-games with aspiration-driven updating rule," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 313-317.
    12. Szabó, György & Hódsági, Kristóf, 2016. "The role of mixed strategies in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 198-206.
    13. Zhao, Jian & Zhang, Ran & An, Tianbo & Zhang, Huizhen & Tong, Daqun & Luo, Xun & An, Jinjin & Wang, Jingrui, 2025. "The effect of heterogeneous perceptions with environmental feedback on spatial social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    14. Ertac, Seda & Gumren, Mert & Gurdal, Mehmet Y., 2020. "Demand for decision autonomy and the desire to avoid responsibility in risky environments: Experimental evidence," Journal of Economic Psychology, Elsevier, vol. 77(C).
    15. Falk Armin & Kosfeld Michael, 2012. "It's all about Connections: Evidence on Network Formation," Review of Network Economics, De Gruyter, vol. 11(3), pages 1-36, September.
    16. Szabó, György & Borsos, István & Szombati, Edit, 2019. "Games, graphs and Kirchhoff laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 416-423.
    17. She, Wenhao & Zhang, Yali & Lu, Yikang & Wu, Haiying & Shi, Lei & Park, Junpyo, 2025. "The impact of higher-order dynamics with intraspecific competition in replicator dynamics on species stability," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    18. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    19. Steven N. Durlauf & Yannis M. Ioannides, 2010. "Social Interactions," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 451-478, September.
    20. Menezes, J. & Moura, B., 2022. "Pattern formation and coarsening dynamics in apparent competition models," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    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:apmaco:v:501:y:2025:i:c:s0096300325001961. 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.