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On a Continuous-Time Game with Incomplete Information

Laboratoire de Mathématiques, U.M.R CNRS 6205 Université de Brest, 29285 Brest cedex, France
Laboratoire de Mathématiques, U.M.R CNRS 6205 Université de Brest, 29285 Brest cedex, France
Pierre.Cardaliaguet{at}univ-brest.fr
Catherine.Rainer{at}univ-brest.fr

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, the authors show that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some martingale measures. The authors also characterizes the optimal martingale measures and computes it explicitly in several examples.

Key Words: continuous-time game; incomplete information; Hamilton-Jacobi equations
History: Received: October 1, 2008; revision received: May 19, 2009;