Attractor States Emerge in Multi-Turn LLM Conversations

Large language models (LLMs) are increasingly used in open-ended multi-agent settings, but the long-run dynamics of model--model interaction remain poorly understood. We study whether open-ended LLM discussions exhibit attractor-like behavior, i.e. topic-independent stable sets of behaviors which conversations settle into. Across 7 LLMs and 20 controversial topics, we compare self-play and mixed-play dyadic debates, tracking trajectories in representation space, discourse traits, and stances. We find self-play trajectories to be model-specific attractors that draw their conversation partners asymmetrically in mixed-play debates, influencing the other models' stylistic choices and behavior. For example, Claude Haiku is a strong attractor of other models in latent space, corresponding to other models taking on its traits like metacommentary, and models like GPT-4.1 nano are especially malleable. Our results suggest that open-ended LLM interactions are partially predictable from model-specific attractors, but shaped by structured and asymmetric partner influence. Overall, our analysis sheds some light on the complex behavior of open-ended multi-agent interaction, which we hope is helpful in designing, predicting, and monitoring autonomous agentic systems in the real world.