Generalized projection dynamics in evolutionary game theory

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Abstract

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative �tness (vector) function both locally and globally. By global (local) ray projection we mean a projection of the vector (close to the unit simplex) unto the unit simplex along a ray through the origin. For these dynamics, we prove that every interior evolutionarily stable strategy is an asymptotically stable �xed point, and that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ these projections on a set of functions related to the relative �tness function which yields a class containing e.g., best- response, logit, replicator, and Brown-Von-Neumann dynamics.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente
Number of pages23
Publication statusPublished - 30 Jan 2009

Publication series

Name
PublisherUniversity of Twente

Keywords

  • IR-97453
  • dynamic and evolutionary stability
  • ray-projection dynamics
  • Evolutionary games

Cite this

Joosten, Reinoud A.M.G. ; Roorda, Berend. / Generalized projection dynamics in evolutionary game theory. Enschede, the Netherlands : University of Twente, 2009. 23 p.
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abstract = "We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative �tness (vector) function both locally and globally. By global (local) ray projection we mean a projection of the vector (close to the unit simplex) unto the unit simplex along a ray through the origin. For these dynamics, we prove that every interior evolutionarily stable strategy is an asymptotically stable �xed point, and that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ these projections on a set of functions related to the relative �tness function which yields a class containing e.g., best- response, logit, replicator, and Brown-Von-Neumann dynamics.",
keywords = "IR-97453, dynamic and evolutionary stability, ray-projection dynamics, Evolutionary games",
author = "Joosten, {Reinoud A.M.G.} and Berend Roorda",
year = "2009",
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address = "Netherlands",

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Joosten, RAMG & Roorda, B 2009, Generalized projection dynamics in evolutionary game theory. University of Twente, Enschede, the Netherlands.

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

Enschede, the Netherlands : University of Twente, 2009. 23 p.

Research output: Book/ReportReportOther research output

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T1 - Generalized projection dynamics in evolutionary game theory

AU - Joosten, Reinoud A.M.G.

AU - Roorda, Berend

PY - 2009/1/30

Y1 - 2009/1/30

N2 - We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative �tness (vector) function both locally and globally. By global (local) ray projection we mean a projection of the vector (close to the unit simplex) unto the unit simplex along a ray through the origin. For these dynamics, we prove that every interior evolutionarily stable strategy is an asymptotically stable �xed point, and that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ these projections on a set of functions related to the relative �tness function which yields a class containing e.g., best- response, logit, replicator, and Brown-Von-Neumann dynamics.

AB - We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative �tness (vector) function both locally and globally. By global (local) ray projection we mean a projection of the vector (close to the unit simplex) unto the unit simplex along a ray through the origin. For these dynamics, we prove that every interior evolutionarily stable strategy is an asymptotically stable �xed point, and that every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. Then, we employ these projections on a set of functions related to the relative �tness function which yields a class containing e.g., best- response, logit, replicator, and Brown-Von-Neumann dynamics.

KW - IR-97453

KW - dynamic and evolutionary stability

KW - ray-projection dynamics

KW - Evolutionary games

M3 - Report

BT - Generalized projection dynamics in evolutionary game theory

PB - University of Twente

CY - Enschede, the Netherlands

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Joosten RAMG, Roorda B. Generalized projection dynamics in evolutionary game theory. Enschede, the Netherlands: University of Twente, 2009. 23 p.