IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v5y2015i2p157-179.html
   My bibliography  Save this article

An Effective Replicator Equation for Games with a Continuous Strategy Set

Author

Listed:
  • M. Ruijgrok
  • Th. Ruijgrok

Abstract

The replicator equation for a two-person symmetric game, which has an interval of the real line as strategy space, is extended with a mutation term. Assuming that the distribution of the strategies has a continuous density, a partial differential equation for this density is derived. The equation is analysed for two examples. A connection is made with the canonical equation from adaptive dynamics and the continuous stable strategy criterion. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • M. Ruijgrok & Th. Ruijgrok, 2015. "An Effective Replicator Equation for Games with a Continuous Strategy Set," Dynamic Games and Applications, Springer, vol. 5(2), pages 157-179, June.
    • Handle: RePEc:spr:dyngam:v:5:y:2015:i:2:p:157-179
    DOI: 10.1007/s13235-014-0118-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-014-0118-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-014-0118-y?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. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
    2. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
    3. Hisashi Ohtsuki, 2011. "Evolutionary Dynamics of the Nash Demand Game: A Diffusion Approach," Dynamic Games and Applications, Springer, vol. 1(3), pages 449-461, September.
    4. Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
    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. Sławomir Plaskacz & Joanna Zwierzchowska, 2019. "Dynamical Systems Associated with the $$\beta $$ β -Core in the Repeated Prisoner’s Dilemma," Dynamic Games and Applications, Springer, vol. 9(1), pages 217-235, March.

    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. Cressman, Ross & Hofbauer, Josef & Riedel, Frank, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers 12/2005, University of Bonn, Bonn Graduate School of Economics (BGSE).
    2. Jean Paul Rabanal, 2017. "On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples," Dynamic Games and Applications, Springer, vol. 7(1), pages 76-92, March.
    3. Wu, Jiabin, 2017. "Political institutions and the evolution of character traits," Games and Economic Behavior, Elsevier, vol. 106(C), pages 260-276.
    4. Jean Rabanal & Daniel Friedman, 2014. "Incomplete Information, Dynamic Stability and the Evolution of Preferences: Two Examples," Dynamic Games and Applications, Springer, vol. 4(4), pages 448-467, December.
    5. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 221-247, June.
    6. Lai, Chong & Li, Rui & Gao, Xiujuan, 2024. "Bank competition with technological innovation based on evolutionary games," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 742-759.
    7. Dharini Hingu, 2020. "Asymptotic stability of strongly uninvadable sets," Annals of Operations Research, Springer, vol. 287(2), pages 737-749, April.
    8. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.
    9. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Dharini Hingu & K. S. Mallikarjuna Rao & A. J. Shaiju, 2018. "Evolutionary Stability of Polymorphic Population States in Continuous Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 141-156, March.
    11. Nassar, Elma & Pardoux, Etienne, 2019. "Small jumps asymptotic of the moving optimum Poissonian SDE," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2320-2340.
    12. Joëlle Noailly, 2008. "Coevolution of economic and ecological systems," Journal of Evolutionary Economics, Springer, vol. 18(1), pages 1-29, February.
    13. Aradhana Narang & A. J. Shaiju, 2019. "Evolutionary Stability of Polymorphic Profiles in Asymmetric Games," Dynamic Games and Applications, Springer, vol. 9(4), pages 1126-1142, December.
    14. Christian Korth, 2009. "Reciprocity—An Indirect Evolutionary Analysis," Lecture Notes in Economics and Mathematical Systems, in: Fairness in Bargaining and Markets, chapter 0, pages 35-55, Springer.
    15. Norman, Thomas W.L., 2012. "Equilibrium selection and the dynamic evolution of preferences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 311-320.
    16. Sivan Frenkel & Yuval Heller & Roee Teper, 2018. "The Endowment Effect As Blessing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(3), pages 1159-1186, August.
    17. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
    18. Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    19. Nonaka, Etsuko & Kuparinen, Anna, 2023. "Limited effects of size-selective harvesting and harvesting-induced life-history changes on the temporal variability of biomass dynamics in complex food webs," Ecological Modelling, Elsevier, vol. 476(C).
    20. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..

    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:5:y:2015:i:2:p:157-179. 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.