Differential Games with Asymmetric and Correlated Information

Differential games with asymmetric information were introduced by Cardaliaguet (SIAM J Control Optim 46:816-838, 2007). As in repeated games with lack of information on both sides (Aumann and Maschler in Repeated games with incomplete information, with the collaboration of R. Stearns, 1995), each player receives a private signal (his type) before the game starts and has a prior belief about his opponent's type. Then, a differential game is played in which the dynamic and the payoff functions depend on both types: each player is thus partially informed about the differential game that is played. The existence of the value function and some characterizations have been obtained under the assumption that the signals are drawn independently. In this paper, we drop this assumption and extend these results to the general case of correlated types. As an application, we provide a new characterization of the asymptotic value of repeated games with incomplete information on both sides, as the unique dual solution of a Hamilton-Jacobi equation.