A differential game with a blind player

Abstract

We consider a zero sum differential game with lack of observation on one side. The initial state of the system is drawn at random according to some probability $\mu_0$ on $\R^N$. Player-I is informed of the initial position of state while player-II knows only $\mu_0$. Moreover Player-I observes Player-II's moves while Player-II is blind and has no further information. We prove that in this game with a terminal payoff the value exists and is characterized as the unique viscosity solution of some Hamilton-Jacobi equation on a space of probability measures.