The replicator equation model for the evolution of individual behaviors in a single-species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional CSS (Continuously Stable Strategy) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger NIS (Neighborhood Invader Strategy) concept is needed if the supports are arbitrary.
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Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number
bgse12_2005.
Length: 52 Date of creation: Apr 2005 Date of revision: Handle: RePEc:bon:bonedp:bgse12_2005
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2004.
"What to Maximize if You Must,"
Discussion Papers
1414, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
[Downloadable!]
HEIFETZ, Aviad & SHANNON, Chris & SPIEGEL, Yossi, 2003.
"What to maximize if you must,"
CORE Discussion Papers
2003047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
[Downloadable!]
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)