Transformers as Game Players: Provable In-context Game-playing Capabilities of Pre-trained Models

TL;DR

This paper demonstrates that pre-trained transformer models can provably learn to approximate Nash equilibria in two-player zero-sum games through in-context learning, extending theoretical understanding to multi-agent settings.

Contribution

It provides the first theoretical guarantees for in-context game-playing capabilities of transformers in multi-agent competitive environments.

Findings

Transformers can approximate Nash equilibria in zero-sum games.

Theoretical guarantees are established for decentralized and centralized learning.

Transformer architecture can realize multi-agent game algorithms like V-learning and VI-ULCB.

Abstract

The in-context learning (ICL) capability of pre-trained models based on the transformer architecture has received growing interest in recent years. While theoretical understanding has been obtained for ICL in reinforcement learning (RL), the previous results are largely confined to the single-agent setting. This work proposes to further explore the in-context learning capabilities of pre-trained transformer models in competitive multi-agent games, i.e., in-context game-playing (ICGP). Focusing on the classical two-player zero-sum games, theoretical guarantees are provided to demonstrate that pre-trained transformers can provably learn to approximate Nash equilibrium in an in-context manner for both decentralized and centralized learning settings. As a key part of the proof, constructional results are established to demonstrate that the transformer architecture is sufficiently rich to realize celebrated multi-agent game-playing algorithms, in particular, decentralized V-learning and centralized VI-ULCB.