When Skills Align: Structural Insights into Nash Stability in Non-Transferable Utility Games

Abstract

In the rapidly evolving field of Artificial Intelligence (AI), multi-agent systems have become crucial for tackling complex, distributed tasks that exceed the capabilities of individual agents. A central challenge in such systems is ensuring the stability of coalitions when agents autonomously collaborate, particularly in scenarios where utility is non-transferable. This study explores the role of skill alignment in achieving Nash stability within Non-Transferable Utility (NTU) games, where each agent's payoff depends on the coalition it forms, and no agent can transfer utility to others.We introduce the concept of a Capability Complementarity Index (CCI) to measure the degree to which agents' skills complement each other. Using this index, we examine how capability complementarity influences coalition stability in multi-agent systems. Our simulations, involving 500 agents with random capability profiles across 10 dimensions, show that coalitions with higher CCI are significantly more likely to achieve Nash stability. Additionally, the results reveal that agents tend to form larger coalitions when their capabilities align well, and such coalitions exhibit fewer defections.These findings provide valuable insights for designing decentralized AI systems, such as autonomous vehicles, cooperative robotics, and distributed sensor networks, where agents must collaborate autonomously without external authority. The study contributes to the theoretical understanding of coalition formation in multi-agent systems and offers practical design principles for creating resilient and efficient AI ecosystems. By emphasizing the importance of skill complementarity, this research helps inform the development of AI systems capable of stable, self-organizing cooperation among agents with heterogeneous capabilities.