Monatshefte für Mathematik

, Volume 110, Issue 3–4, pp 189–206 | Cite as

Dynamical aspects of evolutionary stability

  • Immanuel M. Bomze


Selection is often viewed as a process that maximizes the average fitness of a population. However, there are often constraints even on the phenotypic level which may prevent fitness optimization. Consequently, in evolutionary game theory, models of frequency dependent selection are investigated, which focus on equilibrium states that are characterized by stability (or uninvadability) rather than by optimality. The aim of this article is to relate these stability notions with asymptotic stability in the so-called “replicator dynamics”, by generalizing results, which are well-known for elementary situations, to a fairly general setting applicable, e.g. to complex populations. Moreover, a purely dynamical characterization of evolutionary stability and uninvadability is presented.


Equilibrium State General Setting Game Theory Asymptotic Stability Dynamical Aspect 
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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Immanuel M. Bomze
    • 1
  1. 1.Institut für Statistik und InformatikUniversität WienWienAustria

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