AI agents can coordinate beyond human scale

Large language models (LLMs) are increasingly deployed in collaborative tasks involving multiple agents, forming an "AI agent society: where agents interact and influence one another. Whether such groups can spontaneously coordinate on arbitrary decisions without external influence - a hallmark of self-organized regulation in human societies - remains an open question. Here we investigate the stability of groups formed by AI agents by applying methods from complexity science and principles from behavioral sciences. We find that LLMs can spontaneously form cohesive groups, and that their opinion dynamics is governed by a majority force coefficient, which determines whether coordination is achievable. This majority force diminishes as group size increases, leading to a critical group size beyond which coordination becomes practically unattainable and stability is lost. Notably, this critical group size grows exponentially with the language capabilities of the models, and for the most advanced LLMs, it exceeds the typical size of informal human groups. Our findings highlight intrinsic limitations in the self-organization of AI agent societies and have implications for the design of collaborative AI systems where coordination is desired or could represent a treat.