Existence of Team-Optimal Solutions in Static Teams with Common Information: A Topology of Information Approach

This paper establishes the existence of team-optimal solutions in certain classes of static teams with observation sharing information structures. To establish the existence result, we first construct an equivalent virtual static team (or multiple virtual static teams) with no observation sharing information structure. Then, we establish the existence of a team-optimal solution in the virtual static team, thereby establishing the existence result for the original team. We use the existence result to show that Witsenhausen's counterexample with a certain kind of side information admits a team-optimal solution.