Games with Incomplete Information in Continuous Time and for Continuous Types

We consider a two‐player zero‐sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an auxiliary optimization problem over a set of measure‐valued processes. Then we use this equivalent formulation to characterize the value function as the viscosity solution of a special type of a Hamilton–Jacobi equation. This paper generalizes the results of a previous work of the authors (Math. Oper. Res. 34(4), 769–794, 2009), where only a finite number of possible payoffs is considered.