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Equilibres corrélés, jeux d'évolution et dynamique de populations.

Abstract : This dissertation is divided in three parts. The first part groups contributions to the study of correlated equilibria. We focus on the properties and applications of the dual reduction (Myerson, 1997) and the geometry of Nash equilibria and correlated equilibria. The second part deals with evolutionary dynamics. We investigate the link between strategies belonging to the support of Nash or correlated equilibria and strategies surviving in the long-run. We find that many dynamics, including the replicator and best-response dynamics may eliminate all strategies in the support of correlated equilibria. Elimination of all strategies in the support of Nash equilibria is found to be even more universal, and may occur from almost all initial conditions. The third part consists of a single co-written article, which belongs to the field of theoretical biology. We study aspects of the transition from unicellular to multi-cellular organisms, in particular factors driving germ-soma specialization in volvocine green algae. Lengthier introductions are given at the beginning of each part. The bibliography of part I and part II is disjoint from the bibliography of part III, and is given at the end of part II. Though interconnected, the chapters are essentially self-contained. In particular, the notations and some definitions are recalled each time. This accounts for some repetitions.
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Yannick Viossat. Equilibres corrélés, jeux d'évolution et dynamique de populations.. Mathématiques [math]. Ecole polytechnique X, 2005. Français. ⟨pastel-00002313⟩

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