Do LLMs Beat Nash? Testing Decentralized Coordination in Self-Play Multi-Agent Games

2026-08-12

AI Summary

This study investigates whether large language models can achieve effective coordination surpassing Nash equilibrium in one-shot, multi-agent games without communication or a central controller. The authors construct a self-play benchmark to systematically evaluate the coordination capabilities of 13 models under the assumption that all agents employ the same model. Results demonstrate that two state-of-the-art closed-source models consistently outperform Nash equilibrium in two-player settings, approaching joint optimality, whereas open-source models exhibit limited performance highly dependent on game structure. Coordination efficacy markedly deteriorates in games with four or more players. This work provides the first evidence of the critical influence of model scale and game structure on communication-free coordination among language agents.

Abstract

Large language model agents deployed without a central controller are often assumed to require communication to coordinate their actions. We ask what remains possible without it: when independent instances of the same model cannot communicate, can they still reason about their counterparts well enough to exceed the standard game-theoretic baseline for uncoordinated play? We introduce a benchmark of one-shot, no-communication games in which each of thirteen language models is told only that its counterparts are running the same model and is evaluated against the Nash equilibrium of the underlying game. In two-player matrix games spanning seven archetypes and two to ten actions per player, two frontier-hosted models consistently exceed their Nash benchmark, approaching the optimal joint outcome in several archetypes, while most open-weight models achieve only partial gains that vary sharply by game structure. Performance degrades substantially in team-based games with four or more interchangeable agents, particularly as the action space grows, suggesting that whatever capability drives self-play gains in dyadic games does not transfer to larger multi-agent teams.

Problem

• Large Language Models
• Nash Equilibrium
• Decentralized Coordination
• Multi-Agent Games
• Self-Play

Innovation

• large language models
• multi-agent coordination
• Nash equilibrium
• self-play
• no-communication games