### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 1-26 |

Number of pages | 26 |

Journal | Papers on economics & evolution |

Volume | 2008 |

Issue number | #0811 |

Publication status | Published - 2008 |

### Keywords

- METIS-253804
- projection dynamics
- Evolutionary game theory
- ray projection
- IR-61516
- orthogonal projection
- asymptotical and evolutionary stability

### Cite this

*Papers on economics & evolution*,

*2008*(#0811), 1-26.

}

*Papers on economics & evolution*, vol. 2008, no. #0811, pp. 1-26.

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

Research output: Contribution to journal › Article › Academic › peer-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 -