Revisiting Game Representations: The Hidden Costs of Efficiency in Sequential Decision-making Algorithms

TL;DR

This paper critically examines the efficiency and limitations of current game representations in sequential decision-making algorithms, highlighting the restricted applicability of existing benchmarks and proposing a broader understanding of game models.

Contribution

It identifies the limitations of extensive-form and information-state representations, clarifies the differences with Sequential Bayesian Games, and questions the generalizability of current experimental results.

Findings

Extensive-form representations are memory-inefficient for large games.

Information-state trees limit the class of games that can be efficiently represented.

Many benchmark results are based on a restricted class of Sequential Bayesian Games.

Abstract

Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the extensive-form game formalism, which, as we show, while theoretically sound, is memory-inefficient and computationally intensive in practice. To mitigate these challenges, a popular workaround involves using a specialized representation based on player specific information-state trees. However, as we show, this alternative significantly narrows the set of games that can be represented efficiently. In this study, we identify the set of large games on which modern algorithms have been benchmarked as being naturally represented by Sequential Bayesian Games. We elucidate the critical differences between extensive-form game and sequential Bayesian game representations, both theoretically and empirically. We further argue that the impressive experimental results often cited in the literature may be skewed, as they frequently stem from testing these algorithms only on this restricted class of games. By understanding these nuances, we aim to guide future research in developing more universally applicable and efficient algorithms for sequential decision-making under imperfect information.