# Microscopic dynamics of consensus formation in multi-agent LLM Naming Games

arXiv: https://arxiv.org/abs/2608.02178 · HTML: https://mlsanity.com/paper/2608.02178/

## 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 14 of its 17 references that are in the map.
- First posted on arXiv 3 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, 14 of 14)

- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Simulating Opinion Dynamics with Networks of LLM-based Agents](https://mlsanity.com/paper/2311.09618/) (2023)
- [Cooperate or Collapse: Emergence of Sustainable Cooperation in a Society of LLM Agents](https://mlsanity.com/paper/2404.16698/) (2024)
- [When LLMs Play the Telephone Game: Cultural Attractors as Conceptual Tools to Evaluate LLMs in Multi-turn Settings](https://mlsanity.com/paper/2407.04503/) (2024)
- [Group size effects and collective misalignment in LLM multi-agent systems](https://mlsanity.com/paper/2510.22422/) (2025)
- [Conformity and Social Impact on AI Agents](https://mlsanity.com/paper/2601.05384/) (2026)
- [Conformity Generates Collective Misalignment in AI Agents Societies](https://mlsanity.com/paper/2605.10721/) (2026)
- [Detailed balance in large language model-driven agents](https://mlsanity.com/paper/2512.10047/) (2025)
- [Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networks](https://mlsanity.com/paper/2505.21426/) (2025)
- [Reaching Agreement Among Reasoning LLM Agents](https://mlsanity.com/paper/2512.20184/) (2025)
- [Exploring the Topology and Memory of Consensus: How LLM Agents Agree, Fragment, or Settle When Forming Conventions](https://mlsanity.com/paper/2606.04197/) (2026)
- [Increasing intelligence in AI agents can worsen collective outcomes](https://mlsanity.com/paper/2603.12129/) (2026)
- [Collective Alignment in LLM Multi-Agent Systems: Disentangling Bias from Cooperation via Statistical Physics](https://mlsanity.com/paper/2605.10528/) (2026)
- [SIGN: Schema-Induced Games for Naming](https://mlsanity.com/paper/2510.21855/) (2025)

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

- [Message capacity and claim wording set the transition points of collective truth-finding in language-model networks](https://mlsanity.com/paper/2609.19183/) (2026)

## Abstract (arXiv)

Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature T, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates π(T)!equiv!P(YESmid w∈ Pj) and φ(T)!equiv!P(YESmid wnotin Pj), whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the (π,φ) plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent β(T) in trm conv!~!Nβ shifts with temperature, and the temperature-sensitivity α in tc!~!eα T ranges from ≈,0.67 to ≈,0 across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.