Team Belief DAG: Generalizing the Sequence Form to Team Games for Fast Computation of Correlated Team Max-Min Equilibria via Regret Minimization

TL;DR

This paper introduces the team belief DAG (TB-DAG), a novel convex representation for team strategies in extensive-form games, enabling faster computation of correlated team max-min equilibria through regret minimization.

Contribution

The paper proposes the TB-DAG, a new convex set representation for team strategies that improves computational efficiency and scalability over existing methods.

Findings

TB-DAG can be exponentially smaller than existing representations.

TB-DAG allows for exponentially faster computation of strategies.

Experimental results show state-of-the-art performance on benchmark team games.

Abstract

A classic result in the theory of extensive-form games asserts that the set of strategies available to any perfect-recall player is strategically equivalent to a low-dimensional convex polytope, called the sequence-form polytope. Online convex optimization tools operating on this polytope are the current 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 convex description of the strategy set of the team. In this paper, we provide new complexity results on the computation of optimal strategies for teams, and propose a new representation, coined team belief DAG (TB-DAG), that describes team strategies as a convex set. The TB-DAG enjoys state-of-the-art parameterized complexity bounds, while at the same time enjoying the advantages of efficient regret minimization techniques. We show that TB-DAG can be exponentially smaller and can be computed exponentially faster than all other known representations, and that the converse is never true. Experimentally, we show that the TB-DAG, when paired with learning techniques, yields state of the art on a wide variety of benchmark team games.