标题： 碳定价在交通网络中 显示英文标题

标题： Carbon Pricing in Traffic Networks

摘要： 交通是全球碳排放的重要来源。 在本文中，我们研究如何利用碳定价来引导交通达到符合给定排放预算的均衡状态。 特别是，我们考虑一个具有流量依赖性外部性的通用多商品流模型。 这些外部性可能代表碳排放、进入定价区域或通过可交易信用计划监管的路径。 我们提供了当为每种外部性分配单一价格时，所有可以作为Wardrop均衡实现的流量的完整表征。 更准确地说，我们证明了网络中任何可行流量所能实现的每种外部性预算，也可以通过设置适当的价格作为Wardrop均衡实现。 对于极端和帕累托最小的预算，我们证明存在一些价格，使得所有均衡都遵守预算。 尽管这些特定价格的存在性证明依赖于不动点论证且是非构造性的，但我们证明在均衡最小化凸势函数的情况下，价格可以作为适当凸规划的拉格朗日乘数获得。 在单一外部性的情况下，我们证明由交通流引起的总外部性随着价格的增加而减少。 对于具有单一外部性的递增、连续且分段线性的出行时间函数，我们提供了一个输出多项式算法，用于计算通过定价外部性可实现的所有均衡。 尽管在某些网络中输出大小随输入大小呈指数增长，但我们证明满足给定预算的最小价格可以在多项式时间内计算。 这使得可交易信用计划的市场价格能够高效计算。 总体而言，我们的结果表明，碳定价是一种可行且（在温和假设下）易于处理的方法，可用于在交通网络中实现所有可行的排放目标。 显示英文摘要

摘要： Traffic is a significant source of global carbon emissions. In this paper, we study how carbon pricing can be used to guide traffic towards equilibria that respect given emission budgets. In particular, we consider a general multi-commodity flow model with flow-dependent externalities. These externalities may represent carbon emissions, entering a priced area, or the traversal of paths regulated by tradable credit schemes. We provide a complete characterization of all flows that can be attained as Wardrop equilibria when assigning a single price to each externality. More precisely, we show that every externality budget achievable by any feasible flow in the network can also be achieved as a Wardrop equilibrium by setting appropriate prices. For extremal and Pareto-minimal budgets, we show that there are prices such that all equilibria respect the budgets. Although the proofs of existence of these particular prices rely on fixed-point arguments and are non-constructive, we show that in the case where the equilibrium minimizes a convex potential, the prices can be obtained as Lagrange multipliers of a suitable convex program. In the case of a single externality, we prove that the total externality caused by the traffic flow is decreasing in the price. For increasing, continuous, and piecewise affine travel time functions with a single externality, we give an output-polynomial algorithm that computes all equilibria implementable by pricing the externality. Even though there are networks where the output size is exponential in the input size, we show that the minimal price obeying a given budget can be computed in polynomial time. This allows the efficient computation of the market price of tradable credit schemes. Overall, our results show that carbon pricing is a viable and (under mild assumptions) tractable approach to achieve all feasible emission goals in traffic networks.