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

Cite this

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title = "Generalized projection dynamics in evolutionary game theory",
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.",
keywords = "METIS-253804, projection dynamics, Evolutionary game theory, ray projection, IR-61516, orthogonal projection, asymptotical and evolutionary stability",
author = "Joosten, {Reinoud A.M.G.} and Berend Roorda",
year = "2008",
language = "Undefined",
volume = "2008",
pages = "1--26",
journal = "Papers on economics & evolution",
issn = "1430-4716",
publisher = "Max-Planck-Institut f{\"u}r Wissenschaftsgeschichte",
number = "#0811",

}

Generalized projection dynamics in evolutionary game theory. / Joosten, Reinoud A.M.G.; Roorda, Berend.

In: Papers on economics & evolution, Vol. 2008, No. #0811, 2008, p. 1-26.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Generalized projection dynamics in evolutionary game theory

AU - Joosten, Reinoud A.M.G.

AU - Roorda, Berend

PY - 2008

Y1 - 2008

N2 - 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.

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.

KW - METIS-253804

KW - projection dynamics

KW - Evolutionary game theory

KW - ray projection

KW - IR-61516

KW - orthogonal projection

KW - asymptotical and evolutionary stability

M3 - Article

VL - 2008

SP - 1

EP - 26

JO - Papers on economics & evolution

JF - Papers on economics & evolution

SN - 1430-4716

IS - #0811

ER -