Paul Samuelson's critique and equilibirum concepts 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 languageEnglish
Place of PublicationJena, Germany
PublisherMax Planck Institute of Economics
Number of pages27
Publication statusPublished - 2009

Publication series

NamePapers on Economics & Evolution
PublisherMax Planck Institute of Economics
No.0916
ISSN (Print)1430-4716

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