Microscopic dynamics of consensus formation in multi-agent LLM Naming Games
2026-08-03 • Multiagent Systems
Multiagent Systems
AI summaryⓘ
The authors study how groups of AI language models (LLMs) can agree on shared naming conventions through local interactions. They introduce a simplified model where the listener’s response depends on a randomness level controlled by a 'temperature' parameter, affecting how likely they accept a name. By analyzing two key probabilities, the authors derive conditions for when consensus happens or fails, showing different behaviors based on temperature and model type. They find that the temperature controls how quickly consensus is reached and that this varies across different LLM architectures. Their work uses tools from physics to explain how randomness influences group agreement in decentralized AI systems.
Large Language ModelsNaming GameDecoding TemperatureConsensus DynamicsMean-Field TheoryStochastic ProcessesStatistical PhysicsFinite-Size ScalingAgent-Based ModelsDecentralized Systems
Authors
Cristiano De Nobili, Vijayasri Iyer, Alessandro Codello, Raffaella Burioni
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.