Abstract
This article is concerned with the existence of a value for a zero-sum differential game with an asymmetric information on initial state with an infinite horizon running cost. Before the game begins, an initial state is chosen randomly from a finite set and each player receives a private signal generated by the chosen initial state. The main result is that the game has a value with random non-anticipative strategies with delay and that its value function can be characterized as the unique bounded continuous viscosity solution of a suitable Hamilton–Jacobi–Isaacs equation.
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