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

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 $\alpha$-potential game framework for decentralized CAV control. We show that computing $\alpha$-NE reduces to solving a decentralized control problem, and derive tight bounds of the parameter $\alpha$ based on interaction intensity and asymmetry. We further develop scalable policy gradient algorithms for computing $\alpha$-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.