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

2026-08-03

AI Summary

This study investigates the microscopic mechanisms by which multi-agent large language models (LLMs) achieve consensus in decentralized settings, with a focus on how intrinsic stochasticity influences emergent macroscopic order. By constructing a minimal LLM-based naming game and modulating listener decisions via single-token decoding temperature \( T \), the authors decompose interactions into intra- and extra-inventory channels and introduce, for the first time, methods from statistical physics to formulate a two-timescale mean-field theory that captures consensus dynamics. They analytically derive a critical line condition in the \( (\pi, \phi) \)-plane, revealing decoding temperature as an architecture-dependent control parameter. Consensus is observed across three open-source LLM architectures, uncovering three distinct listener mechanisms; the convergence time scaling exponent \( \beta(T) \) and temperature sensitivity \( \alpha \) vary with architecture, with \( \alpha \) ranging between 0 and 0.67.

Abstract

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 $π(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $φ(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, 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 $t_{\rm conv}\!\sim\!N^β$ shifts with temperature, and the temperature-sensitivity $α$ in $t_c\!\sim\!e^{αT}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.

Problem

• consensus formation
• microscopic dynamics
• Large Language Models
• Naming Game
• stochasticity

Innovation

• LLM Naming Game
• decoding temperature
• mean-field theory
• consensus formation
• stochastic multi-agent systems