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Deterministic evolutionary dynamics: a unifying approach

Author

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  • Reinoud Joosten

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

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.

Suggested Citation

  • Reinoud Joosten, 1996. "Deterministic evolutionary dynamics: a unifying approach," Journal of Evolutionary Economics, Springer, vol. 6(3), pages 313-324.
    • Handle: RePEc:spr:joevec:v:6:y:1996:i:3:p:313-324
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    Citations

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    Cited by:

    1. Gordon Burt, 1997. "Cultural Convergence in Historical Cultural Space-Time," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 21(4), pages 291-305, December.
    2. Caichun Chai & Eilin Francis & Tiaojun Xiao, 2021. "Supply chain dynamics with assortative matching," Journal of Evolutionary Economics, Springer, vol. 31(1), pages 179-206, January.
    3. Reinoud Joosten & Berend Roorda, 2011. "On evolutionary ray-projection dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 147-161, October.
    4. Velasco Morente, Francisco & Nadal Morales, Purificación & González Abril, Luis & Ortega Ramírez, Juan Antonio, 2009. "Bifurcaciones de codimensión 2 en un modelo dinámico del mercado potencial y actual: aplicación al mercado cervecero español = Bifurcations of Codimension 2 in a Dynamical Model of Current and Potenti," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 7(1), pages 77-94, June.
    5. Hofbauer, Josef & Sandholm, William H., 2009. "Stable games and their dynamics," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1665-1693.4, July.
    6. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    7. Sean Holly & Emiliano Santoro, 2007. "Financial Fragility, Heterogeneous Firms and the Cross Section of the Business Cycle," Money Macro and Finance (MMF) Research Group Conference 2006 96, Money Macro and Finance Research Group.
    8. Reinoud Joosten & Berend Roorda, 2011. "Attractive evolutionary equilibria," Papers on Economics and Evolution 2011-17, Philipps University Marburg, Department of Geography.
    9. Markus Pasche, 2001. "Equilibrium Concepts for Boundedly Rational Behavior in Games," Working Paper Series B 2001-03, Friedrich Schiller University of Jena, School of of Economics and Business Administration.
    10. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Philipps University Marburg, Department of Geography.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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