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Dynamic Team Theory of Stochastic Differential Decision Systems with Decentralized Noiseless Feedback Information Structures via Girsanov's Measure Transformation

In this paper we generalized static team theory to dynamic team theory, in the context of stochastic differential decision system with decentralized noiseless feedback information structures. We apply Girsanov's theorem to transformed the initial stochastic dynamic team problem to an equivalent team problem, under a reference probability space, with state process and information structures independent of any of the team decisions. Subsequently, we show, under certain conditions, that continuous-time and discrete-time stochastic dynamic team problems, can be transformed to equivalent static team problems, although computing the optimal team strategies using this method might be computational intensive. Therefore, we propose an alternative method, by deriving team and Person-by-Person (PbP) optimality conditions, via the stochastic Pontryagin's maximum principle, consisting of forward and backward stochastic differential equations, and a set of conditional variational Hamiltonians with respect to the information structures of the team members. Finally, we relate the backward stochastic differential equation to the value process of the stochastic team problem.