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In this paper, we demonstrate the existence of team-optimal strategies forstatic teams under observation-sharing information structures. Assuming thatagents can access shared observations, we begin by converting the team probleminto an equivalent centralized stochastic control problem through theintroduction of a topology on policies. We subsequently apply conventionalmethods from stochastic control to prove the existence of team-optimalstrategies. This study expands upon the widely recognized common informationapproach for team problems, originally designed for discrete scenarios, andadapts it to a more abstract continuous framework. The primary difficulty inthis context is to establish the appropriate topology on policies.

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