Common Information Approach for Static Team Problems with Polish Spaces and Existence of Optimal Policies

In this paper, we demonstrate the existence of team-optimal strategies for static teams under observation-sharing information structures. Assuming that agents can access shared observations, we begin by converting the team problem into an equivalent centralized stochastic control problem through the introduction of a topology on policies. We subsequently apply conventional methods from stochastic control to prove the existence of team-optimal strategies. This study expands upon the widely recognized common information approach for team problems, originally designed for discrete scenarios, and adapts it to a more abstract continuous framework. The primary difficulty in this context is to establish the appropriate topology on policies.