发表机构
Columbia University; Imperial College London（哥伦比亚大学; 帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出 $\alpha$-势博弈框架，将异构自动驾驶车辆去中心化决策的近似纳什均衡计算简化为单势函数最小化，并通过车辆特定缩放收紧近似，实验验证了其在多种交通场景下的有效性。
AI 中文摘要
我们研究了异构自动驾驶车辆之间的非合作多车博弈，其中每辆车采用基于自身状态的去中心化闭环策略，并优化一个通过可能不对称的交互权重依赖于其他车辆的目标函数。我们开发了一个 $\alpha$-势博弈框架，将近似纳什均衡（NE）的计算简化为单个辅助 $\alpha$-势函数的最小化。我们显式构造了该 $\alpha$-势，证明了其极小值的存在性，并刻画了以交互不对称性表示的均衡近似误差 $\alpha$。我们进一步引入车辆特定缩放以减少有效交互不对称性，从而收紧均衡近似，并在重要情况下，尽管存在不对称交互，也能恢复精确的纳什均衡。我们还推导了势选择策略的社会效率保证，揭示了交互结构如何塑造最坏情况下的效率。数值实验展示了该框架在捕获异构车辆交互、碰撞与障碍物避免、不同交通配置下的车道变换与超车，以及基于优先级的交叉口通行方面的灵活性。
英文摘要
We study noncooperative multi-vehicle games among heterogeneous autonomous vehicles, where each vehicle adopts a decentralized closed-loop policy based on its own state, and optimizes an objective that depends on other vehicles through potentially asymmetric interaction weights. We develop an $α$-potential game framework that reduces the computation of an approximate Nash equilibrium (NE) to the minimization of a single auxiliary $α$-potential function. We explicitly construct this $α$-potential, establish the existence of its minimizers, and characterize the equilibrium approximation error $α$ in terms of interaction asymmetry. We further introduce vehicle-specific scaling to reduce the effective interaction asymmetry, thereby tightening the equilibrium approximation and, in important cases, recovering an exact NE despite asymmetric interactions. We also derive social-efficiency guarantees for the potential-selected policies, revealing how the interaction structure shapes worst-case efficiency. Numerical experiments demonstrate the flexibility of the framework in capturing heterogeneous vehicle interactions, collision and obstacle avoidance, lane changing and overtaking under different traffic configurations, and priority-based intersection crossing.
