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Deterministic evolutionary dynamics: A unifying approach

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Abstract

We tackle three components of evolutionary modelling: payoffs, dynamical systems and equilibrium concepts. Firstly, we merely require that fitness functions are continuous. Secondly, we examine very general classes of dynamics. Thirdly, we give useful parallels to the Nash equilibrium and the evolutionarily stable strategy. Under (weakly) sign-compatible dynamics the change in population share of every (at least one) subgroup present in the population corresponds in sign with its relative fitness. At a saturated equilibrium, each subgroup with positive population share has highest fitness. We examine two evolutionary stability concepts: the evolutionarily stable equilibrium and the generalized evolutionarily stable state.

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Authors and Affiliations

  1. MERIT, Department of Mathematics, University of Limburg, P.O. Box 616, 6200 MD, Maastricht, The Netherlands

    Reinoud Joosten

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  1. Reinoud Joosten
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I owe much to the anonymous refereeing process. I thank J. Oechssler, B. Verspagen, H. Peters, F. Thuijsman, D. Talman, E. van Damme, A. van den Elzen, R. Nelson, H. van der Stel for comments, criticism or encouragement. Audiences in Tel Aviv (EARIE), and Tilburg (CentER) are thanked for suggestions. I am grateful to the Jerusalem Summer School on Economic Theory for its hospitality in 1994 (Rationality of Belief and Action in the Economy) and 1995 (Evolution and Learning in Games and Economics).

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Joosten, R. Deterministic evolutionary dynamics: A unifying approach. J Evol Econ 6, 313–324 (1996). https://doi.org/10.1007/BF01193636

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