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: topic-independent stable sets of behaviors into which conversations settle. Across seven LLMs and twenty 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. Our results suggest that open-ended LLM interactions are partially predictable from model-specific attractors, but shaped by structured and asymmetric partner influence.