Is Congestion Pricing Effective for Traffic Jams?

AYRAT, Elzat; Xiaoyan, LIN · 2022 · DOAJ

DOI: 10.7307/ptt.v34i1.3815

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Summary

This paper investigates the effectiveness of congestion pricing in multi-stakeholder transportation networks, specifically addressing the conflict that arises when various autonomous regions or entities with differing objectives compete to set tolls. The authors argue that traditional multi-objective optimization models, which assume a single leader decides on pricing, fail to account for the autonomy of stakeholders and the potential for conflicting interests. This gap is significant because real-world road pricing implementations often fail due to a lack of support from stakeholders who feel excluded from the decision-making process. The study aims to determine whether classical game-theoretic solution concepts, particularly Nash equilibrium, can provide a stable and fair framework for toll setting among competing actors, including road users modeled as stakeholders. The authors develop a multi-leader, multi-follower game model formulated as an Equilibrium Problem with Equilibrium Constraints (EPEC). In this framework, multiple stakeholders (leaders) simultaneously set tolls to minimize their individual cost functions, which may include travel time, emissions, noise, or revenue, while considering user benefits. Road users (followers) react to these tolls by choosing routes according to Wardrop’s user equilibrium. The mathematical model assumes separable, strictly convex link cost functions and elastic demand. The authors analyze the existence of pure and mixed Nash equilibria in this non-cooperative setting, comparing unrestricted toll scenarios with those constrained by non-negative tolls. They also examine cooperative game solutions to identify stable and profitable coalitions. The primary finding is that a pure Nash equilibrium generally does not exist in the road pricing game when stakeholders have conflicting objectives. The authors prove that if leaders can set unrestricted tolls (including negative values), no equilibrium is reachable because any player can unilaterally adjust their toll to achieve their ideal flow pattern, preventing stability. Even with fixed demand and non-negative toll constraints, a Nash equilibrium is not guaranteed. Consequently, the non-cooperative approach fails to provide a stable solution. However, the paper demonstrates that cooperative game solutions can identify specific coalitions that are reachable, stable, and profitable for the involved actors. These cooperative outcomes offer a viable alternative to the unstable non-cooperative Nash scenarios. The significance of this research lies in its challenge to the applicability of standard Nash equilibrium concepts in decentralized road pricing. By showing that independent toll setting leads to instability, the paper highlights the necessity for cooperation among stakeholders. The findings suggest that for congestion pricing to be effective and accepted, mechanisms must be established to facilitate collaboration and coalition formation among competing entities, including the representation of user interests. This provides a theoretical foundation for designing policy frameworks that mitigate the feelings of unfairness and conflict that have historically hindered the implementation of road pricing schemes in various cities.

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• traffic density