When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games, where all vehicle contribute identically to congestion. However, with the proliferation of autonomous vehicles and driver-assistance technology, vehicles become heterogeneous in how they contribute to road latency. This magnifies the potential inefficiencies due to selfish routing and invalidates traditional tolling methods. To address this, we consider a network of parallel roads where the latency on each road is an affine function of the quantity of flow of each vehicle type. We provide tolls (which differentiate between vehicle types) which are guaranteed to minimize social cost at equilibrium. The tolls are a function of a calculated optimal routing; to enable this tolling, we prove that some element in the set of optimal routings has a lack of cycles in a graph representing the way vehicles types share roads. We then show that unless a planner can differentiate between vehicle types in the tolls given, the resulting equilibrium can be unboundedly worse than the optimal routing, and that marginal cost tolling fails in our setting.

中文翻译：

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多类型混合自治交通网络的最优收费

当自私的用户共享一个道路网络并最小化他们的个人出行成本时，他们达到的平衡可能比社会最优路线更糟糕。在传统的拥堵游戏中，通行费通常用于减轻这种影响，在这种游戏中，所有车辆对拥堵的贡献都是相同的。然而，随着自动驾驶汽车和驾驶员辅助技术的普及，车辆在如何导致道路延迟方面变得多样化。这会放大由于自私路由而导致的潜在低效率，并使传统的收费方法无效。为了解决这个问题，我们考虑了一个平行道路网络，其中每条道路上的延迟是每种车辆类型流量的仿射函数。我们提供通行费（区分车辆类型），保证在平衡时将社会成本降至最低。通行费是计算出的最佳路线的函数；为了实现这种收费，我们证明了最佳路线集中的某些元素在表示车辆类型共享道路方式的图中缺少循环。然后我们表明，除非规划者可以区分给定的通行费中的车辆类型，否则由此产生的均衡可能会比最佳路线更糟糕，并且在我们的设置中边际成本通行费是失败的。