AI summaryⓘ
The authors studied how networks form when many language models (LLM agents) pick who to work with on their own. They found that popular agents tend to get even more connections, but sometimes weaker agents can end up very important, which they call a glass-ceiling effect. They created a math model to explain how these networks settle into stable patterns and designed a way for agents to choose collaborators based on a utility inspired by attention mechanisms. Their experiments with 100 agents showed that who becomes central depends on factors like model size and task, and that aligning popularity with ability can improve overall group performance. This work helps understand how different LLMs interact and form communication patterns over time.
Large Language ModelsCollaborative NetworksPreferential AttachmentCentralityGlass-Ceiling EffectMean-Field DynamicsCross-AttentionUtility FunctionNetwork FormationAgent-Based Modeling
Abstract
We investigate the emergence of structural disparities in networks of collaborating large language model (LLM) agents. When LLM agents autonomously choose collaborators, the resulting communication network exhibits preferential-attachment dynamics: agents that are already prominent become increasingly likely to attract additional connections. In some cases, weaker LLM agents (agents with smaller base model or older version) can disproportionately occupy central and influential network positions relative to stronger LLM agents. We interpret this as a type-dependent glass-ceiling effect (GCE). We model the network of LLM agents as a time-evolving sequence of directed weighted graphs, where the vector-valued edge weights represent cumulative tokens exchanged, number of interaction rounds, and reasoning effort. Using a contraction mapping argument on the mean-field dynamics, we prove that the importance (centrality) of each agent type converges to a unique stable equilibrium. To ground the model in LLM decision mechanisms, we introduce a cross-attention-inspired utility for collaborator selection. This utility specifies the local connection dynamics and, together with the mean-field model, yields a predictive characterization of the limiting network structure and its type-dependent centrality gaps. To validate the theory, we develop an experimental testbed with 100 LLM agents. Our experiments show that autonomous network formation can generate persistent centrality disparities, with their magnitude and direction depending on model family, model size, system-prompt design, and task context. They further show that the effect of preferential attachment depends on its alignment with model capability: reinforcing it improves collective performance when stronger agents become central, whereas weakening it improves performance when network dynamics instead favor weaker agents.