LLM Agent Societies: Stability, Chaos, and Adaptive Learning

Emmanouil-Vasileios Vlatakis-Gkaragkounis

Keywords: Multi-agent learning, LLM societies, adaptive learning rates, chaotic behavior, instability, emergent dynamics, turbulence, self-play, equilibrium, stability analysis

TL;DR: Large-scale LLM agent societies remain unstable and unpredictable, with adaptive learning rates failing to prevent chaotic behaviors, necessitating deeper stability analysis.

Abstract:

Multi-agent learning in LLM agent societies is inherently more complex, unstable, and unpredictable than single-agent optimization. Large-scale interactions between multiple language models—each trained on different objectives and responding to dynamic contexts—introduce significant challenges in achieving stability, coherence, and meaningful convergence in dialogue, decision-making, and reasoning tasks.

To address this, numerous heuristics and specialized techniques have been developed, particularly in the area of self-play and emergent coordination among LLM agents. One widely studied approach is the use of dynamically adaptive learning rates, which allow agents to adjust their response strategies based on the evolving discourse and interactions. While these methods have been successful in small-scale conversational models, their effectiveness remains far less understood in large agent societies, where thousands of LLMs interact in open-ended, multi-step reasoning environments.

Recent research suggests that fixed adaptation mechanisms can lead to instability and chaotic behaviors in multi-agent reinforcement learning settings. This issue becomes even more pronounced in LLM societies, where interactions evolve over complex and high-dimensional latent spaces. In this work, we show that chaos and instability persist even when agents employ adaptive strategies, such as Multiplicative Weight Updates (MWU), which is commonly used to balance exploration and exploitation in dialogue generation. Surprisingly, even in settings where agents have only two competing response strategies, the system can exhibit turbulent and unpredictable behaviors.

At a technical level, the emergent behaviors of LLM societies differ from classical reinforcement learning dynamics due to their non-autonomous evolution—where agents continuously update their internal representations based on new data, past interactions, and external fine-tuning. Our analysis extends beyond conventional Li-Yorke period-three techniques, exploring the role of invariant structures, volume expansion, and turbulent information flow in shaping the stability of LLM interactions.

We complement our theoretical findings with experimental results, demonstrating that even slight variations in agent architectures, learning rules, or interaction patterns can lead to widely differing and unpredictable conversational behaviors. These results highlight the urgent need for principled stability analysis in large-scale LLM interactions and pave the way for designing more robust, interpretable, and controllable multi-agent AI ecosystems.

Submission Number: 2