IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v388y2021ics0096300320304549.html
   My bibliography  Save this article

Kinetic approach to the collective dynamics of the rock-paper-scissors binary game

Author

Listed:
  • Pouradier Duteil, Nastassia
  • Salvarani, Francesco

Abstract

This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.

Suggested Citation

  • Pouradier Duteil, Nastassia & Salvarani, Francesco, 2021. "Kinetic approach to the collective dynamics of the rock-paper-scissors binary game," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320304549
    DOI: 10.1016/j.amc.2020.125496
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320304549
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125496?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. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    2. repec:hhs:iuiwop:487 is not listed on IDEAS
    3. Iwamura, Yoshiro & Nagashima, Keisuke & Tanimoto, Jun, 2020. "Evolutionary dynamics of a 3-strategy game: Cooperator, defector and costly cooperative loner strategic types," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    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. Zhong, Yue & Lai, Shaoyong & Hu, Chunhua, 2021. "Investigations to the dynamics of wealth distribution in a kinetic exchange model," Applied Mathematics and Computation, Elsevier, vol. 404(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. Dufwenberg, Martin, 1997. "Some relationships between evolutionary stability criteria in games," Economics Letters, Elsevier, vol. 57(1), pages 45-50, November.
    2. Lichi Zhang & Yanyan Jiang & Junmin Wu, 2022. "Evolutionary Game Analysis of Government and Residents’ Participation in Waste Separation Based on Cumulative Prospect Theory," IJERPH, MDPI, vol. 19(21), pages 1-16, November.
    3. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    4. Gu, Tianqi & Xu, Weiping & Liang, Hua & He, Qing & Zheng, Nan, 2024. "School bus transport service strategies’ policy-making mechanism – An evolutionary game approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(C).
    5. Petrohilos-Andrianos, Yannis & Xepapadeas, Anastasios, 2017. "Resource harvesting regulation and enforcement: An evolutionary approach," Research in Economics, Elsevier, vol. 71(2), pages 236-253.
    6. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    7. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.
    8. Meng Ding & Hui Zeng, 2022. "Multi-Agent Evolutionary Game in the Recycling Utilization of Sulfate-Rich Wastewater," IJERPH, MDPI, vol. 19(14), pages 1-20, July.
    9. Kulsum, Umma & Alam, Muntasir & Kamrujjaman, Md., 2024. "Modeling and investigating the dilemma of early and delayed vaccination driven by the dynamics of imitation and aspiration," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    10. Guohui Song & Yongbin Wang, 2021. "Mainstream Value Information Push Strategy on Chinese Aggregation News Platform: Evolution, Modelling and Analysis," Sustainability, MDPI, vol. 13(19), pages 1-17, October.
    11. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2021. "The evolution of morals under indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 126(C), pages 251-277.
    12. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    13. Angelo Antoci & Simone Borghesi & Marcello Galeotti, 2013. "Environmental options and technological innovation: an evolutionary game model," Journal of Evolutionary Economics, Springer, vol. 23(2), pages 247-269, April.
    14. Hui Yu & Wei Wang & Baohua Yang & Cunfang Li, 2019. "Evolutionary Game Analysis of the Stress Effect of Cross-Regional Transfer of Resource-Exhausted Enterprises," Complexity, Hindawi, vol. 2019, pages 1-16, November.
    15. Galor, Oded & Klemp, Marc, 2014. "The Biocultural Origins of Human Capital Formation," IZA Discussion Papers 8433, Institute of Labor Economics (IZA).
    16. Moreira, Helmar Nunes & Araujo, Ricardo Azevedo, 2011. "On the existence and the number of limit cycles in evolutionary games," MPRA Paper 33895, University Library of Munich, Germany.
    17. Xie, Yunya & Zhang, Shuhua & Zhang, Zhipeng & Bu, Hongyu, 2020. "Impact of binary social status with hierarchical punishment on the evolution of cooperation in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    18. Li, Jingjing & Wang, Zhaoxin & Li, Hui & Jiao, Jianling, 2024. "Which policy can effectively promote the formal recycling of power batteries in China?," Energy, Elsevier, vol. 299(C).
    19. Müller, Stephan, 2014. "The evolution of inequality aversion in a simplified game of life," University of Göttingen Working Papers in Economics 219, University of Goettingen, Department of Economics.
    20. Witte, Björn-Christopher, 2012. "Fund managers - Why the best might be the worst: On the evolutionary vigor of risk-seeking behavior," Economics Discussion Papers 2012-20, Kiel Institute for the World Economy (IfW Kiel).

    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:388:y:2021:i:c:s0096300320304549. 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.