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In this paper, we establish the existence of team-optimal policies for staticteams and a class of sequential dynamic teams. We first consider the staticteam problems and show the existence of optimal policies under certainregularity conditions on the observation channels by introducing a topology onthe set of policies. Then we consider sequential dynamic teams and establishthe existence of an optimal policy via the static reduction method ofWitsenhausen. We apply our findings to the well-known counterexample ofWitsenhausen and the Gaussian relay channel problem.

A topology for Team Policies and Existence of Optimal Team Policies in Stochastic Team Theory