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

arXiv: https://arxiv.org/abs/2608.12547 · HTML: https://mlsanity.com/paper/2608.12547/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 10 of 10)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://mlsanity.com/paper/2503.01743/) (2025)
- [Gemma 4 Technical Report](https://mlsanity.com/paper/2607.02770/) (2026)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- ["Other-Play" for Zero-Shot Coordination](https://mlsanity.com/paper/2003.02979/) (2020)
- [LLM-Coordination: Evaluating and Analyzing Multi-agent Coordination Abilities in Large Language Models](https://mlsanity.com/paper/2310.03903/) (2023)
- [Decentralized Multi-Agent Goal Assignment for Path Planning using Large Language Models](https://mlsanity.com/paper/2510.23824/) (2025)

## Built on by (most cited first, 1 of 1)

- [Shared and structured inputs undermine collective random choice by reasoning AI agents](https://mlsanity.com/paper/2610.09667/) (2026)

## Abstract (arXiv)

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.