Carbon Pricing in Traffic Networks

2025-08-12

AI Summary

This paper investigates how carbon pricing can steer traffic flows toward a Wardrop equilibrium consistent with a prescribed emission budget. We propose a modeling framework integrating multi-commodity flow and externality pricing, which— for the first time—fully characterizes the set of equilibria attainable via carbon pricing and proves that a pricing policy exists for any feasible emission target. Theoretically, we establish monotonicity: total emissions decrease monotonically with increasing carbon price under a single externality, and we derive a closed-form expression for the minimum compliant carbon price. Algorithmically, we develop a polynomial-time solution method based on Lagrangian duality and convex potential function optimization, enabling efficient carbon pricing design and supporting tradable credit mechanisms. Our results provide both a rigorous theoretical foundation and practical computational tools for precise, tractable regulation of transportation-sector carbon emissions.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Combinatorial Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

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.

Problem

• How carbon pricing guides traffic to meet emission budgets
• Characterizing flows achievable as Wardrop equilibria with pricing
• Computing minimal prices for emission budgets efficiently

Innovation

• Carbon pricing guides traffic to emission equilibria
• Prices derived from convex program Lagrange multipliers
• Polynomial-time algorithm computes minimal pricing