$α$-Potential Games for Decentralized Control of Connected and Automated Vehicles

Abstract: Designing scalable and safe control strategies for large populations of connected and automated vehicles (CAVs) requires accounting for strategic interactions among heterogeneous agents under decentralized information. While dynamic games provide a natural modeling framework, computing Nash equilibria (NEs) in large-scale settings remains challenging, and existing mean-field game approximations rely on restrictive assumptions that fail to capture collision avoidance and heterogeneous behaviors. This paper proposes an $α$-potential game framework for decentralized CAV control. We show that computing $α$-NE reduces to solving a decentralized control problem, and derive tight bounds of the parameter $α$ based on interaction intensity and asymmetry. We further develop scalable policy gradient algorithms for computing $α$-NEs using decentralized neural-network policies. Numerical experiments demonstrate that the proposed framework accommodates diverse traffic flow models and effectively captures collision avoidance, obstacle avoidance, and agent heterogeneity.