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Correlated equilibria, evolutionary games and population dynamics

Abstract : This dissertation consists of three parts, the first two in game theory and the third one in theoretical biology. The first part studies the correlated equilibrium concept, due to Aumann. We first investigate the properties and applications of the dual reduction technique, introduced by Myerson. We then use this technique to show that the set of games with a unique correlated equilibrium is open, which is not true for Nash equilibrium, and to characterize the class of games with a Nash equilibrium in the relative interior of the correlated equilibrium polytope. In the two-player case, this class of games generalizes two-person zero-sum games. Two other contributions are also presented.

The second part deals with evolutionary games and studies the link between evolutionary dynamics and static strategic concepts. We show in particular that evolutionary dynamics may eliminate all strategies in the support of at least one correlated equilibrium. This occurs under any monotonic dynamics whose vector field depends continuously on the payoffs, and for open sets of games and initial conditions. Furthermore, elimination of all strategies in the support of Nash equilibria occurs under any smooth myopic adjustment dynamics and, under the replicator dynamics or the best-response dynamics, from almost all initial conditions.

The third part, co-written, studies the factors driving cell differentiation, and especially germ-soma differentiation in volvocine green algae.
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Submitted on : Wednesday, April 26, 2006 - 5:18:23 PM
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  • HAL Id : tel-00012181, version 1

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Yannick Viossat. Correlated equilibria, evolutionary games and population dynamics. Mathematics [math]. Ecole Polytechnique X, 2005. English. ⟨tel-00012181⟩

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