Group size effects and collective misalignment in LLM multi-agent systems

TL;DR

This work demonstrates that group size affects the dynamics in a non-linear way, revealing model-dependent dynamical regimes and establishes group size as a key driver of multi-agent dynamics and highlights the need to consider population-level effects when deploying LLM-based systems at scale.

Abstract

Multi-agent systems of large language models (LLMs) are rapidly expanding across domains, introducing dynamics not captured by single-agent evaluations. Yet, existing work has mostly contrasted the behavior of a single agent with that of a collective of fixed size, leaving open a central question: how does group size shape dynamics? Here, we move beyond this dichotomy and systematically explore outcomes across the full range of group sizes. We focus on multi-agent misalignment, building on recent evidence that interacting LLMs playing a simple coordination game can generate collective biases absent in individual models. First, we show that collective bias is a deeper phenomenon than previously assessed: interaction can amplify individual biases, introduce new ones, or override model-level preferences. Second, we demonstrate that group size affects the dynamics in a non-linear way, revealing model-dependent dynamical regimes. Finally, we develop a mean-field analytical approach and show that, above a critical population size, simulations converge to deterministic predictions that expose the basins of attraction of competing equilibria. These findings establish group size as a key driver of multi-agent dynamics and highlight the need to consider population-level effects when deploying LLM-based systems at scale.

Figures (35)

• Figure 1: Interaction can amplify, induce, or override individual bias. From left to right columns, the word pairs that populations coordinate on are: {American, Mexican}, {White, African}, and {straight, gay}. These cases illustrate bias amplification, induction from neutrality, and bias reversal, respectively. Top row (a–c): Llama populations; bottom row (d–f): GPT populations. All simulations use a population size of $N=24$. The upper plots in each panel display representative trajectories of word competition in 1000 simulation runs, where blue and orange lines indicate the frequency of unique convention choices over time (based on the previous $N$ interactions). Colored circles at $t=0$ denote the initial individual bias, with black indicating neutrality. Where possible, at least ten trajectories are shown for each consensus outcome (strong or weak convention); when fewer runs converged, all available trajectories are displayed. Solid and dotted lines show the mean dynamics of runs that converged on the strong and weak conventions, respectively. In all cases, the strong word is represented by blue trajectories (from left to right: Mexican, African, gay). The lower bar plots summarize individual and collective bias: individual bias reflects agents’ pre-interaction preferences, and collective bias shows the fraction of runs that reached consensus on each convention.
• Figure 2: Collective bias depends on both model and convention. Panels show individual and collective bias for four LLMs (clockwise from top left: Phi, GPT, Qwen, and Llama) in populations of size $N=24$, for the word pairs indicated in the legend. Individual bias corresponds to an agent’s selection probability at the start of the game with empty memory, while collective bias denotes the proportion of 1000 runs that reached consensus on the option in bold. Error bars (SEM) are smaller than the marker size. The dashed line shows the theoretical prediction from the minimal Naming Game with binary options and individual bias. Points along the gray dotted line at $x = 0.5$ indicate symmetry breaking, where neutral individual preferences produce biased collective outcomes. Points within the shaded pink regions correspond to bias reversal, where collective interactions overturn the individual preference.
• Figure 3: Population size effects on collective bias. For all convention pairs tested, collective preference for a given convention increases with population size until convergence becomes deterministic. The individual bias is reported at $N=1$. Error bars (SEM) are smaller than the marker size. Across population sizes, all runs reached consensus except in three cases: in Llama populations, the convergence rate decreases beyond a certain $N$ for {old, young} and {less, more}, and in small Qwen populations, a few runs failed to converge for the word pair {husband, wife}. See SI Figs. \ref{['fig: non-consensus_fraction_410']}-\ref{['fig: non-consensus_dynamics_1161']} for word competition dynamics and precise convergence fractions for these cases.
• Figure 4: Coordination dynamics become increasingly deterministic for larger populations. Each column shows the temporal dynamics of word competition (top row), and the probability density function of the consensus time (bottom row) for trajectories that reached consensus. Specifically, each column shows the results at different population sizes, for GPT populations coordinating on the word pair {White, African}. The PDFs in the bottom row are constructed from 100,000 observations in total, where blue circles and orange triangles correspond to trajectories that converged on the strong (African) and weak (White) word, respectively. The dotted red line indicates the shortest possible consensus time allowed by the convergence criterion, $t=3$. The top row shows the usage fraction at each population round of the strong (blue lines) and weak (orange lines) words in up to 25 trajectories for each consensus state. The collective bias toward the word African grows with population size as (from left to right columns, up to 3 s.f.): 0.626, 0.720, 0.981, 1.00.
• Figure S1: Accuracy of model responses to prompt comprehension questions. For each model, 100 random memory states were generated. Each memory state was used to initialize the game state of a random agent, which was then presented with the comprehension questions. For each question, the fraction of correct responses across all agents is shown. Error bars represent the standard error of the mean.