Generalized projection dynamics in evolutionary game theory

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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.
Original languageUndefined
Pages (from-to)1-26
Number of pages26
JournalPapers on economics & evolution
Volume2008
Issue number#0811
Publication statusPublished - 2008

Keywords

  • METIS-253804
  • projection dynamics
  • Evolutionary game theory
  • ray projection
  • IR-61516
  • orthogonal projection
  • asymptotical and evolutionary stability

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