### Abstract

Original language | English |
---|---|

Pages (from-to) | 1-27 |

Number of pages | 27 |

Journal | Papers on economics & evolution |

Volume | 2009 |

Issue number | #0916 |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- IR-87198
- METIS-262192

### Cite this

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*Papers on economics & evolution*, vol. 2009, no. #0916, pp. 1-27.

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

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

TY - JOUR

T1 - Paul Samuelson's critique and equilibirum concepts in evolutionary game theory

AU - Joosten, Reinoud A.M.G.

PY - 2009

Y1 - 2009

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 - IR-87198

KW - METIS-262192

M3 - Article

VL - 2009

SP - 1

EP - 27

JO - Papers on economics & evolution

JF - Papers on economics & evolution

SN - 1430-4716

IS - #0916

ER -