NfgTransformer: Equivariant Representation Learning for Normal-form Games

Abstract

Normal-form games (NFGs) are fundamental subjects of game theoretic analysis that describe strategic interactions between players. While NFGs are typically represented as payoff tensors, any permutation of player actions describes an identical game. We propose NfgTransformer, a general-purpose query-key-value architecture that exploits the equivariance inherent to this data modality. We show the efficacy of our approach in a range of downstream tasks, including equilibrium solving, deviation-gain estimation and ranking on synthetic and standard games. Beyond strong quantitative results, we show that our model internally developed a recognisable pattern of iterative equilibrium refinement when solving for a Nash Equilibrium in a suite of GAMUT games. We hope our work can serves as an effective bridge to bring scalable learning techniques to game theoretic analysis.

Authors

Siqi Liu, Luke Marris, Ian Gemp, Georgios Piliouras, Nicolas Heess

Venue

ICLR 2024