[2510.06903] When Machines Meet Each Other: Network Effects and the Strategic Role of History in Multi-Agent AI

The study [2510.06903] examines how GPT-5-based large language model (LLM) agents behave in a canonical network-effect game where economic theory predicts convergence to a fulfilled expectation equilibrium (FEE), in which realized participation matches a common expectation across agents . The researchers designed an experimental framework involving 50 heterogeneous LLM agents that interact repeatedly under systematically varied network-effect strengths ($$\beta \in \{0.25, 0.75\}$$), price trajectories, and decision-history lengths . Results show that LLM agents systematically diverge from FEE: they underestimate participation at low prices and overestimate it at high prices, maintaining persistent forecast dispersion rather than converging to equilibrium .

A key finding is that history plays a critical strategic role in shaping agent expectations, in contrast to classical economic models where past outcomes are treated as sunk . When agents have access to historical data, the structure of that history significantly influences coordination. Simple monotonic histories—where price trends follow a steady upward or downward path—help stabilize expectations and reduce forecasting errors, especially as the history window lengthens . For instance, under weak network effects, expanding the history from one to thirteen rounds reduces RMSE from 9.031 to 2.486 in decreasing-price scenarios . In contrast, non-monotonic or random histories amplify divergence and path dependence, disrupting convergence entirely .

Regression analyses reveal that price is the dominant driver of deviation from FEE, while history moderates this effect by dampening sensitivity to extreme prices . Network effects do not act independently but amplify contextual distortions, increasing the impact of price-driven biases and heterogeneity in agent behavior . These findings contribute to the evaluation of AI agents in economic games by demonstrating that equilibrium reasoning does not emerge endogenously in current LLMs; instead, their strategic behavior is shaped by the interplay of incentives, internal heterogeneity, and historical context, all modulated by network effects . This highlights a structural departure from rational-expectations theory and suggests that machine cognition requires a rethinking of equilibrium models in multi-agent systems .

This paper explores the emergent strategic behaviors of GPT-5-based Large Language Model (LLM) agents when deployed in a network-effect game. The authors focus on the agents' ability to achieve "fulfilled expectation equilibria"—a state where agents' predictions about the actions of others align perfectly with reality, leading to stable coordination. By simulating these agents within a game where the utility of decisions depends on the collective choices of the network, the study investigates how effectively advanced LLMs can navigate complex economic environments that require recursive reasoning and anticipation of peer behavior.

A key contribution of the work is the analysis of the strategic role of history in facilitating this convergence. The findings suggest that the availability and structure of historical interaction data are critical determinants in whether agents successfully coordinate or succumb to coordination failures. The research demonstrates that while GPT-5 agents possess the capability to model the expectations of other agents, their success is highly contingent on the context provided by past network states, offering new insights into the fragility or robustness of AI-driven coordination mechanisms.

This research is significant as it advances the methodology for evaluating AI agents in economic games, moving beyond simple adversarial setups to complex, interdependent systems. As AI agents increasingly operate in digital marketplaces and decentralized networks, understanding their capacity to reach and maintain equilibria is vital for predicting system stability and efficiency. The study provides a foundational framework for assessing how advanced foundation models handle the nuances of economic theory, particularly regarding expectation formation and network externalities.

Summary of [2510.06903] When Machines Meet Each Other: Network Effects and the Strategic Role of History in Multi-Agent AI

This paper investigates the behavior of GPT-5-based large language model (LLM) agents in a network-effect game, where agents interact strategically under conditions of fulfilled expectation equilibria (FEEs). The study examines how these agents converge to equilibrium under varying degrees of network externalities—where the value of an agent’s action depends on the collective behavior of others—and explores the strategic role of historical context in shaping decision-making. By deploying agents in repeated interactions, the authors assess whether LLMs can internalize expectations about others' actions and adapt dynamically, akin to human players in economic games.

The key contributions of this work include: 1. Empirical validation of FEE convergence: The paper demonstrates that GPT-5 agents can approximate FEEs in network-effect settings, even when initial beliefs are misaligned, highlighting their capacity for strategic reasoning under uncertainty. 2. Role of history in decision-making: The study finds that agents’ past interactions significantly influence their strategy formation, suggesting that temporal context is a critical factor in multi-agent coordination. 3. Implications for AI evaluation: By framing LLM agents as participants in economic games, the work offers a novel framework for assessing strategic intelligence beyond traditional benchmarks, with potential applications in decentralized systems, market simulation, and cooperative AI design.

This research matters because it bridges game theory, AI alignment, and economic modeling, providing insights into how autonomous agents might navigate complex, interdependent environments. The findings have implications for designing self-aware AI systems that account for network effects and historical dependencies, which are increasingly relevant in domains like automated negotiation, financial markets, and multi-agent collaboration.