Properties of the value function for nonzero-sum differential game

The talk is concerned with the nonzero-sum differential games. We study value (multi)function and its link with punushment strategies and Hamilton-Jacobi PDES. We present the examples showing that - multivalueness is an intrinsic property of nonzero-sum differential games. - the value function can be discontinuous - both players can increas their outcomes using punishment strategies.