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Existence of Team-Optimal Strategies in Teams With Countable Observation Spaces

Team problems, in which multiple agents act to minimize a common expected cost function, are generally intractable. The problem of establishing the existence of team-optimal strategies has received significant attention in the past decade. In this article, we present a proof of the existence of team-optimal strategies in a class of teams in which observations are realized in a countable set and are shared among the agents and the action sets are noncompact. We derive sufficient conditions under which optimal deterministic strategies exist.