Existence of Value for a Differential Game with Incomplete Information and Revealing

This article is devoted to the existence of value for a zero-sum differential game with incomplete information on initial state with partial revealing of information and with a running cost. Before the game begins, an initial state is chosen from among several states, and both players do not know this initial state until the dynamic system reaches a fixed target during the game. The main result is the existence of value for the game defined with nonanticipative strategies with delay. Moreover, the value is the unique bounded continuous viscosity solution of a suitable Hamilton--Jacobi--Isaacs equation.