Differential games with imperfect information.

Summary This thesis studies different types of games with asymmetric information. For games with incomplete information on both sides, we present a discrete approximation of the value function based on the Mertens-Zamir operator. We also give an optimal strategy for the one-sided incomplete information game where players optimize a current payoff independent of the system state. In the framework of non-zero-sum games, we give the characterization of Nash equilibrium payments in mixed strategies, which is very similar to the "folk theorem" of repeated games. These equilibrium payments are in fact Nash equilibrium payments in publicly correlated strategies. Finally, we study a type of imperfectly observed game where one of the players is blind. We establish the existence of the value, characterized as the unique solution of a Hamilton-Jacobi equation in the Wasserstein space.