IDEAS home Printed from https://ideas.repec.org/a/wsi/acsxxx/v06y2003i02ns0219525903000815.html
   My bibliography  Save this article

Survival And Extinction In The Replicator Model: Dynamics And Statistics

Author

Listed:
  • SEBASTIÁN BOUZAT

    (Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Río Negro, Argentina)

  • DAMIÁN H. ZANETTE

    (Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Río Negro, Argentina)

Abstract

We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its average interaction with the rest of the system. The role of the interaction pattern of the ecosystem in defining survival and extinction probabilities is emphasized.

Suggested Citation

  • Sebastián Bouzat & Damián H. Zanette, 2003. "Survival And Extinction In The Replicator Model: Dynamics And Statistics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 223-240.
    • Handle: RePEc:wsi:acsxxx:v:06:y:2003:i:02:n:s0219525903000815
    DOI: 10.1142/S0219525903000815
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219525903000815
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219525903000815?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. Larry Samuelson, 1998. "Evolutionary Games and Equilibrium Selection," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262692198, 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. Kyle Hyndman & Antoine Terracol & Jonathan Vaksmann, 2009. "Learning and sophistication in coordination games," Experimental Economics, Springer;Economic Science Association, vol. 12(4), pages 450-472, December.
    2. Veller, Carl & Hayward, Laura K., 2016. "Finite-population evolution with rare mutations in asymmetric games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 93-113.
    3. Ingela Alger & Laurent Lehmann, 2023. "Evolution of Semi-Kantian Preferences in Two-Player Assortative Interactions with Complete and Incomplete Information and Plasticity," Dynamic Games and Applications, Springer, vol. 13(4), pages 1288-1319, December.
    4. Huw Dixon & Ernesto Somma, "undated". "Coordination and Equilibrium selection in mean defined supermodular games under payoff monotonic selection dynamics," Discussion Papers 99/37, Department of Economics, University of York.
    5. Villani, Salvatore, 2008. "L’emergenza dei tre lustri, la salma contesa e il gioco dell’Ultimatum. Alcune riflessioni sui problemi che caratterizzano le decisioni pubbliche in Italia [The 15-years-long emergency, the burial-," MPRA Paper 29857, University Library of Munich, Germany, revised 14 Sep 2008.
    6. Anastasios Xepapadeas & Yannis Petrohilos-Andrianos, 2013. "On the Evolution of Compliance and Regulation with Tax Evading Agents," DEOS Working Papers 1325, Athens University of Economics and Business.
    7. Angelo Antoci & Alessandro Fiori Maccioni & Paolo Russu, 2016. "The Ecology of Defensive Medicine and Malpractice Litigation," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-15, March.
    8. Berger, Ulrich & Grüne, Ansgar, 2016. "On the stability of cooperation under indirect reciprocity with first-order information," Games and Economic Behavior, Elsevier, vol. 98(C), pages 19-33.
    9. Dufwenberg, Martin, 1997. "Some relationships between evolutionary stability criteria in games," Economics Letters, Elsevier, vol. 57(1), pages 45-50, November.
    10. 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.
    11. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    12. 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).
    13. Petrohilos-Andrianos, Yannis & Xepapadeas, Anastasios, 2017. "Resource harvesting regulation and enforcement: An evolutionary approach," Research in Economics, Elsevier, vol. 71(2), pages 236-253.
    14. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    15. 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.
    16. 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.
    17. 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).
    18. 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.
    19. 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.
    20. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.

    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:wsi:acsxxx:v:06:y:2003:i:02:n:s0219525903000815. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/acs/acs.shtml .

    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.