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Generalized projection dynamics in evolutionary game theory

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Listed:
  • Reinoud Joosten
  • Berend Roorda

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.

Suggested Citation

  • 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.
    • Handle: RePEc:esi:evopap:2008-11
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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. 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.
    3. 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.

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    More about this item

    Keywords

    evolutionary game theory; projection dynamics; orthogonal projection; ray projection; asymptotical and evolutionary stability Length 27 pages;
    All these keywords.

    JEL classification:

    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • 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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