Games with incomplete information in continuous time and for continuous types

Details Games with incomplete information in continuous time and for continuous types Games with incomplete information in continuous time and for continuous types

2012-02-22

arxiv.org/abs/1202.4845v1

Mathematics

Probability

Scientific paper

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, where only a finite number of possible payoffs is considered.

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