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
Pages (from-to)1-27
Number of pages27
JournalPapers on economics & evolution
Volume2009
Issue number#0916
Publication statusPublished - 2009

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Evolutionary Game Theory
Projection
Half line
Generalized Projection
Evolutionarily Stable Strategy
Logit
Unit
Asymptotically Stable
Interior
Correspondence
Fixed point
Concepts

Keywords

  • IR-87198
  • METIS-262192

Cite this

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Paul Samuelson's critique and equilibirum concepts in evolutionary game theory. / Joosten, Reinoud A.M.G.

In: Papers on economics & evolution, Vol. 2009, No. #0916, 2009, p. 1-27.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - 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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KW - METIS-262192

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