On evolutionary ray-projection dynamics

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Abstract

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner.
Original languageEnglish
Pages (from-to)147-161
Number of pages15
JournalMathematical methods of operations research
Volume74
Issue number2
DOIs
Publication statusPublished - 2011

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Half line
Projection
Fixed point
Game theory
Terminology
Interior
Evolutionarily Stable Strategy
Evolutionary Game Theory
Evolutionary Dynamics
Interior Point
Fitness Function
Asymptotically Stable
Fitness
Evolutionary
Unit

Keywords

  • IR-85163
  • METIS-275414

Cite this

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On evolutionary ray-projection dynamics. / Joosten, Reinoud A.M.G.; Roorda, Berend.

In: Mathematical methods of operations research, Vol. 74, No. 2, 2011, p. 147-161.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - On evolutionary ray-projection dynamics

AU - Joosten, Reinoud A.M.G.

AU - Roorda, Berend

N1 - Open Access

PY - 2011

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AB - We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner.

KW - IR-85163

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U2 - 10.1007/s00186-010-0342-1

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