### 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 language | Undefined |
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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

Joosten, R. A. M. G., & Roorda, B. (2008). Generalized projection dynamics in evolutionary game theory.

*Papers on economics & evolution*,*2008*(#0811), 1-26.