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Generalized projection dynamics in evolutionary game theory

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  • Reinoud Joosten
  • Berend Roorda
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    Abstract

    We introduce a new kind of projection dynamics by employing a ray-projection both locally and globally. By global (local) we mean a projection of a vector (close to the unit simplex) unto the unit simplex along a ray through the origin. Using a correspondence between local and global ray-projection dynamics we prove that every interior evolutionarily stable strategy is an asymptotically stable fixed point. We also show that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ several projections on a wider set of functions derived from the payoff structure. This yields an interesting class of so-called generalized projection dynamics which contains best-response, logit, replicator, and Brown-Von-Neumann dynamics among others.

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    Bibliographic Info

    Paper provided by Philipps University Marburg, Department of Geography in its series Papers on Economics and Evolution with number 2008-11.

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    Date of creation: Oct 2008
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    Handle: RePEc:esi:evopap:2008-11

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    Phone: 064212824257
    Fax: 064212828950
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    Web page: http://www.uni-marburg.de/fb19/
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    Keywords: evolutionary game theory; projection dynamics; orthogonal projection; ray projection; asymptotical and evolutionary stability Length 27 pages;

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    Cited by:
    1. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution, Philipps University Marburg, Department of Geography 2009-16, Philipps University Marburg, Department of Geography.

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