On the Existence of Optimal Policies for a Class of Static and Sequential Dynamic Teams

In this paper, we identify sufficient conditions under which static teams and a class of sequential dynamic teams admit team-optimal solutions. We first investigate the existence of optimal solutions in static teams where the observations of the decision makers are conditionally independent given the state and satisfy certain regularity conditions. Building on these findings and the static reduction method of Witsenhausen, we then extend the analysis to sequential dynamic teams. In particular, we show that a large class of dynamic linear-quadratic-Gaussian (LQG) teams, including the vector version of the well-known Witsenhausen’s counterexample and the Gaussian relay channel problem viewed as a dynamic team, admit team-optimal solutions. Results in this paper substantially broaden the class of stochastic control problems with nonclassical information known to have optimal solutions.