A Topology for Policies in Decentralized Stochastic Control and Existence of Optimal Policies

In this paper, we introduce a topology for policies in decentralized stochastic control models to establish the existence of team-optimal policies for both static and a class of sequential dynamic teams. We first consider the static team problems and show the existence of optimal policies under the assumption that the observation channels have densities and are continuous with respect to the total variation distance. Then we consider sequential dynamic teams and establish the existence of an optimal policy via the static reduction method of Witsenhausen. We apply our findings to the well-known counterexample of Witsenhausen and the Gaussian relay channel.