Some examples of medium field games.

Summary Mean field game theory was introduced in 2006 by Jean-Michel Lasry and Pierre-Louis Lions. It allows the study of game theory in certain configurations where the number of players is too large to hope for a practical resolution. We study the theory of mean-field games on graphs based on the work of Olivier Guéant which we will extend to more general Hilbertian forms. We will also study the links between K-means and mean-field games, which will in principle allow us to propose new algorithms for K-means using numerical resolution techniques specific to mean-field games. Finally, we will study a mean-field game, namely the "meeting start time" problem by extending it to situations where agents can choose between two meetings. We will study analytically and numerically the existence and multiplicity of solutions of this problem.