Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space

Ross Cressman, Josef Hofbauer and Frank Riedel

No 12/2005, Bonn Econ Discussion Papers from University of Bonn, Bonn Graduate School of Economics (BGSE)

Abstract: 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.

Keywords: Adaptive dynamics; CSS; NIS; replicator equation; local superiority; strategy dominance; measure dynamics; weak topology (search for similar items in EconPapers)
Date: 2005
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://www.econstor.eu/bitstream/10419/22918/1/bgse12_2005.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zbw:bonedp:122005

Access Statistics for this paper

More papers in Bonn Econ Discussion Papers from University of Bonn, Bonn Graduate School of Economics (BGSE) Contact information at EDIRC.
Bibliographic data for series maintained by ZBW - Leibniz Information Centre for Economics ().