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On evolutionary ray-projection dynamics

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  • Reinoud Joosten
  • Berend Roorda

Abstract

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991 ), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner. Copyright The Author(s) 2011

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:74:y:2011:i:2:p:147-161
    DOI: 10.1007/s00186-010-0342-1
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    References listed on IDEAS

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    Cited by:

    1. Reinoud Joosten & Berend Roorda, 2011. "Attractive evolutionary equilibria," Papers on Economics and Evolution 2011-17, Philipps University Marburg, Department of Geography.
    2. Marc Harper & Dashiell Fryer, 2015. "Lyapunov Functions for Time-Scale Dynamics on Riemannian Geometries of the Simplex," Dynamic Games and Applications, Springer, vol. 5(3), pages 318-333, September.
    3. Parna Parsapour-Moghaddam & Armaghan Abed-Elmdoust & Reza Kerachian, 2015. "A Heuristic Evolutionary Game Theoretic Methodology for Conjunctive Use of Surface and Groundwater Resources," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(11), pages 3905-3918, September.

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