A Marriage between Adversarial Team Games and 2-player Games: Enabling Abstractions, No-regret Learning, and Subgame Solving

TL;DR

This paper introduces a novel game representation called team-public-information that simplifies the analysis of sequential adversarial team games, enabling the use of tools like abstractions and no-regret learning to compute strategies more efficiently.

Contribution

It proposes a new team-public-information representation that makes complex team games more explainable and computationally manageable, bridging the gap with 2-player game techniques.

Findings

The new representation is payoff equivalent to the original game.

Techniques to generate compact representations from extensive form.

Experimental results show improved performance over state-of-the-art methods.

Abstract

\emph{Ex ante} correlation is becoming the mainstream approach for \emph{sequential adversarial team games}, where a team of players faces another team in a zero-sum game. It is known that team members' asymmetric information makes both equilibrium computation \textsf{APX}-hard and team's strategies not directly representable on the game tree. This latter issue prevents the adoption of successful tools for huge 2-player zero-sum games such as, \emph{e.g.}, abstractions, no-regret learning, and subgame solving. This work shows that we can recover from this weakness by bridging the gap between sequential adversarial team games and 2-player games. In particular, we propose a new, suitable game representation that we call \emph{team-public-information}, in which a team is represented as a single coordinator who only knows information common to the whole team and prescribes to each member an action for any possible private state. The resulting representation is highly \emph{explainable}, being a 2-player tree in which the team's strategies are behavioral with a direct interpretation and more expressive than the original extensive form when designing abstractions. Furthermore, we prove payoff equivalence of our representation, and we provide techniques that, starting directly from the extensive form, generate dramatically more compact representations without information loss. Finally, we experimentally evaluate our techniques when applied to a standard testbed, comparing their performance with the current state of the art.