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Quelques exemples de jeux à champ moyen

Abstract : The mean field game theory was introduced in 2006 by Jean-Michel Lasry and Pierre-Louis Lions. It allows us to study the game theory in some situations where the number of players is too high to be able to be solved in practice. We will study the mean field game theory on graphs by learning from the studies of Oliver Guéant which we will extend to more generalized forms of Hilbertian. We will also study the links between the K-means and the mean field game theory. In principle, this will offer us new algorithms for solving the K-means thanks to the techniques of numerical resolutions of the mean field games. Findly, we will study a mean field game called the "starting time of a meeting". We will extend it to situations where the players can choose between two meetings. We will study analytically and numerically the existence and multiplicity of the solutions to this problem.
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Submitted on : Saturday, February 10, 2018 - 12:36:28 PM
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Jean-Luc Coron. Quelques exemples de jeux à champ moyen. Equations aux dérivées partielles [math.AP]. Université Paris sciences et lettres, 2017. Français. ⟨NNT : 2017PSLED032⟩. ⟨tel-01705969⟩

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