When Machines Meet Each Other: Network Effects and the Strategic Role of History in Multi-Agent AI

As artificial intelligence (AI) enters the agentic era, large language models (LLMs) are increasingly deployed as autonomous agents that interact with one another rather than operate in isolation. This shift raises a fundamental question: how do machine agents behave in interdependent environments where outcomes depend not only on their own choices but also on the coordinated expectations of peers? To address this question, we study LLM agents in a canonical network-effect game, where economic theory predicts convergence to a fulfilled expectation equilibrium (FEE). We design an experimental framework in which 50 heterogeneous GPT-5-based agents repeatedly interact under systematically varied network-effect strengths, price trajectories, and decision-history lengths. The results reveal that LLM agents systematically diverge from FEE: they underestimate participation at low prices, overestimate at high prices, and sustain persistent dispersion. Crucially, the way history is structured emerges as a design lever. Simple monotonic histories-where past outcomes follow a steady upward or downward trend-help stabilize coordination, whereas nonmonotonic histories amplify divergence and path dependence. Regression analyses at the individual level further show that price is the dominant driver of deviation, history moderates this effect, and network effects amplify contextual distortions. Together, these findings advance machine behavior research by providing the first systematic evidence on multi-agent AI systems under network effects and offer guidance for configuring such systems in practice.