We consider the asymptotic value of two person zero sum repeated games with general evaluations of the stream of stage payoffs. We show existence for incomplete information games, splitting games and absorbing games. The technique of proof consists in embedding the discrete repeated game into a...

This paper is devoted to a new approach of differential games with state constraints. We explain a new method, general enough to study discontinuous problems but efficient enough to provide numerical schemes. We present this method in a game of kind: the target problem and in a game of degree:...

This article is devoted to a survey of results for differential games obtained through Viability Theory. We recall the basic theory for differential games (obtained in the 1990s), but we also give an overview of recent advances in the following areas : games with hard constraints, stochastic...

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, the authors show that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some martingale measures. The authors also characterize the...

This survey paper presents some new advances in theoretical aspects of differential game theory. We particular focus on three topics: differential games with state constraints; backward stochastic differential equations approach to stochastic differential games; differential games with...

We investigate a two-player zero-sum stochastic differential game in which the players have an asymmetric information on the random payoff. We prove that the game has a value and characterize this value in terms of dual viscosity solutions of some second order Hamilton-Jacobi equation.

Le maxmin pour une certaine classe de jeux répétés à observation imparfaite est obtenu comme la solution d'un problème d'optimisation défini sur l'ensemble des distributions de probabilités sous contraintes d'entropie. Cette article offre une méthode pour résoudre un tel problème dans...

We give new proofs of existence of the limit of the discounted values for two person zero-sum games in the following frameworks: incomplete information, absorbing, recursive. The idea of these new proofs is to use some comparison criteria.

Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.