Recent advancements in vehicle autonomy have drawn interest in understanding the impact of autonomous vehicles on traffic systems. In this paper, we study a traffic assignment problem in a mixed-autonomy setting where both human-driven and autonomous vehicles coexist. We model the interaction as a simultaneous routing game where human drivers are self-interested and aim to minimize their own travel times, while autonomous agents are altruistic and aim to minimize the total social cost. The standard nonatomic congestion game analysis establishes the existence of equilibrium to this game under convex cost functions, and does not have any implication of its uniqueness. In this work, we formulate the equilibrium as a variational inequality (VI), which enables us to establish the equilibrium existence without convexity assumption, and guarantees the uniqueness of the aggregated link flow and social cost at equilibrium under a specific class of cost functions. Leveraging this VI framework, we provide sufficient conditions under which including autonomous agents improves, deteriorates, or has no effect on social cost. While the possibility of deterioration has been established in prior work, our results complement existing worst-case bounds by explicitly characterizing sufficient conditions under which each outcome occurs, thereby providing a deeper understanding of mixed-autonomy traffic systems. Furthermore, we consider a centralized scenario where a social planner optimizes the routing of autonomous agents, and show that the same equilibrium is achieved as in the decentralized scenario when assuming convex costs.Finally, we conduct numerical experiments that illustrate how social cost changes with the amount of autonomous vehicles under different system parameters.

翻译：近年来车辆自主性的进展引起了人们对自动驾驶车辆对交通系统影响的关注。本文研究了混合自主环境下的交通分配问题，其中人类驾驶车辆与自动驾驶车辆共存。我们将交互建模为同时路由博弈，其中人类驾驶员以自利方式行动，旨在最小化自身行程时间，而自主代理具有利他性，旨在最小化总体社会成本。标准非原子拥塞博弈分析表明，在凸成本函数下该博弈存在均衡，但未涉及唯一性。在本工作中，我们将均衡表述为变分不等式（VI），这使我们能够在无凸性假设下确立均衡的存在性，并在特定成本函数类下保证均衡状态下聚合链路流和社会成本的唯一性。利用该VI框架，我们提供了包含自主代理对社会成本产生改善、恶化或无影响效果的充分条件。尽管先前工作已确认恶化的可能性，我们的结果通过显式刻画每种结果发生的充分条件，补充了现有的最坏情况边界，从而加深了对混合自主交通系统的理解。此外，我们考虑集中式情景，其中社会规划者优化自主代理的路由，并证明在假设凸成本时，该情景达到与分散式情景相同的均衡。最后，通过数值实验展示了社会成本如何随不同系统参数下自动驾驶车辆数量的变化而变化。