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Normal Forms and Unfoldings of Singular Strategy Functions

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  • 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
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    References listed on IDEAS

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    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.
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