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A classic result in the theory of extensive-form games asserts that the setof strategies available to any perfect-recall player is strategicallyequivalent to a low-dimensional convex polytope, called the sequence-formpolytope. Online convex optimization tools operating on this polytope are thecurrent state-of-the-art for computing several notions of equilibria in games,and have been crucial in landmark applications of computational game theory.However, when optimizing over the joint strategy space of a team of players,one cannot use the sequence form to obtain a strategically-equivalent convexdescription of the strategy set of the team. In this paper, we provide newcomplexity results on the computation of optimal strategies for teams, andpropose a new representation, coined team belief DAG (TB-DAG), that describesteam strategies as a convex set. The TB-DAG enjoys state-of-the-artparameterized complexity bounds, while at the same time enjoying the advantagesof efficient regret minimization techniques. We show that TB-DAG can beexponentially smaller and can be computed exponentially faster than all otherknown representations, and that the converse is never true. Experimentally, weshow that the TB-DAG, when paired with learning techniques, yields state of theart on a wide variety of benchmark team games.

Team Belief DAG: A Concise Representation for Team-Correlated Game-Theoretic Decision Making