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We consider a two-player zero-sum game with integral payoff and withincomplete information on one side, where the payoff is chosen among acontinuous set of possible payoffs. We prove that the value function of thisgame is solution of an auxiliary optimization problem over a set ofmeasure-valued processes. Then we use this equivalent formulation tocharacterize the value function as the viscosity solution of a special type ofa Hamilton-Jacobi equation. This paper generalizes the results of a previouswork of the authors, where only a finite number of possible payoffs isconsidered.

Games with incomplete information in continuous time and for continuous types