Non classical information and optimality in continuous-time dynamic team problems

This paper is devoted to the study of optimality criteria in dynamic team problems where the decision makers have noisy observations of the instantaneous state and no memory. Thus the information structure is non classical for two reasons: on the one hand because each decision maker has no access to the observations of the other decision makers, and on the other hand because of his lack of memory. We develop in the cases with and without diffusion, a generalized dynamic programming method giving raise to efficient optimality characterizations via generalized Hamiltonians minimizations, Hamiltonians containing a "signalling term". This theory is applied to a linear quadratic and a nonlinear example and to the famous Witsenhausen\´s counterexample.