IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v5y2015i2p180-213.html
   My bibliography  Save this article

Normal Forms and Unfoldings of Singular Strategy Functions

Author

Listed:
  • Amit Vutha
  • Martin Golubitsky

Abstract

We study adaptive dynamics strategy functions by defining a form of equivalence that preserves key properties of these functions near singular points (such as whether or not a singularity is an evolutionary or a convergent stable strategy). Specifically, we compute and classify normal forms and low codimension universal unfoldings of these functions. These calculations lead to a classification of local pairwise invasibility plots that can be expected in systems with two parameters. This problem is complicated because the allowable coordinate changes at such points are restricted by the specific nature of strategy functions; hence the needed singularity theory is not the standard one. We also show how to use the singularity theory results to help study a specific adaptive game: a generalized hawk—dove game studied previously by Dieckmann and Metz. Copyright The Author(s) 2015

Suggested Citation

  • Amit Vutha & Martin Golubitsky, 2015. "Normal Forms and Unfoldings of Singular Strategy Functions," Dynamic Games and Applications, Springer, vol. 5(2), pages 180-213, June.
    • Handle: RePEc:spr:dyngam:v:5:y:2015:i:2:p:180-213
    DOI: 10.1007/s13235-014-0116-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-014-0116-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-014-0116-0?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. 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.
    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. 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.
    2. Joëlle Noailly, 2008. "Coevolution of economic and ecological systems," Journal of Evolutionary Economics, Springer, vol. 18(1), pages 1-29, February.
    3. Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    4. 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).
    5. 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).
    6. Peña, Jorge & González-Forero, Mauricio, 2020. "Eusociality through conflict dissolution via maternal reproductive specialization," IAST Working Papers 20-110, Institute for Advanced Study in Toulouse (IAST).
    7. Boettiger, Carl & Dushoff, Jonathan & Weitz, Joshua S., 2010. "Fluctuation domains in adaptive evolution," Theoretical Population Biology, Elsevier, vol. 77(1), pages 6-13.
    8. Dercole, Fabio & Prieu, Charlotte & Rinaldi, Sergio, 2010. "Technological change and fisheries sustainability: The point of view of Adaptive Dynamics," Ecological Modelling, Elsevier, vol. 221(3), pages 379-387.
    9. U. Dieckmann & M. Doebeli, 1999. "On the Origin of Species by Sympatric Speciation," Working Papers ir99013, International Institute for Applied Systems Analysis.
    10. Svardal, Hannes & Rueffler, Claus & Hermisson, Joachim, 2015. "A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous environments," Theoretical Population Biology, Elsevier, vol. 99(C), pages 76-97.
    11. Hammerstein, Peter & Leimar, Olof, 2015. "Evolutionary Game Theory in Biology," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. Durrett, Rick & Mayberry, John, 2010. "Evolution in predator-prey systems," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1364-1392, July.
    13. Johansson, Jacob & Ripa, Jörgen & Kuckländer, Nina, 2010. "The risk of competitive exclusion during evolutionary branching: Effects of resource variability, correlation and autocorrelation," Theoretical Population Biology, Elsevier, vol. 77(2), pages 95-104.
    14. Champagnat, Nicolas, 2006. "A microscopic interpretation for adaptive dynamics trait substitution sequence models," Stochastic Processes and their Applications, Elsevier, vol. 116(8), pages 1127-1160, August.
    15. Hernán Darío Toro-Zapata & Gerard Olivar-Tost, 2018. "Mathematical Model For The Evolutionary Dynamic Of Innovation In City Public Transport Systems," Copernican Journal of Finance & Accounting, Uniwersytet Mikolaja Kopernika, vol. 7(2), pages 77-98.
    16. Wu, Jiabin, 2017. "Political institutions and the evolution of character traits," Games and Economic Behavior, Elsevier, vol. 106(C), pages 260-276.
    17. E. Kisdi & F.J.A. Jacobs & S.A.H. Geritz, 2000. "Red Queen Evolution by Cycles of Evolutionary Branching and Extinction," Working Papers ir00030, International Institute for Applied Systems Analysis.
    18. Fritsch, Coralie & Campillo, Fabien & Ovaskainen, Otso, 2017. "A numerical approach to determine mutant invasion fitness and evolutionary singular strategies," Theoretical Population Biology, Elsevier, vol. 115(C), pages 89-99.
    19. Benjamin Wölfl & Hedy te Rietmole & Monica Salvioli & Artem Kaznatcheev & Frank Thuijsman & Joel S. Brown & Boudewijn Burgering & Kateřina Staňková, 2022. "The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer," Dynamic Games and Applications, Springer, vol. 12(2), pages 313-342, June.
    20. Mauricio González-Forero, 2024. "Evolutionary–developmental (evo-devo) dynamics of hominin brain size," Nature Human Behaviour, Nature, vol. 8(7), pages 1321-1333, July.

    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:180-213. 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.