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...

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...

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...

In the present paper we investigate the problem of the existence of a value for differential games without Isaacs condition. For this we introduce a suitable concept of mixed strategies along a partition of the time interval, which are associated with classical nonanticipative strategies (with...