From Aggregate Observations to Social Optimum: An Adaptive Pricing Scheme in Heterogeneous Congestion Games

TL;DR

This paper proposes an adaptive pricing scheme in heterogeneous congestion games that guides traffic towards a social optimum using aggregate observations, ensuring stability despite limited information and diverse user preferences.

Contribution

It introduces a novel pricing approach that aligns externalities with taxes over time, ensuring global stability of the social optimum under aggregate observation constraints.

Findings

Long-term social optimum can be achieved with aggregate data

Heterogeneous VOT complicates externality-based pricing

Full-information pricing may fail to stabilize the social optimum

Abstract

This study investigates an adaptive pricing scheme aimed at achieving an efficient state in a traffic congestion game characterized by a diverse population of road users. While the planner possesses knowledge of players' preferences, their ability to observe only aggregate states limits the implementation of differentiated taxes. We propose a pricing approach that aligns taxes with the true values of externalities over time, ensuring global stability of the social optimum through replicator dynamics. Our findings suggest that the planner, despite being unable to accurately assess externalities at each moment, can still navigate the economy toward a long-term social optimum by adjusting the disaggregated state based on aggregate observations, while acknowledging the challenges posed by heterogeneous value of time (VOT) among drivers. We also find that a pricing mechanism that incorporates the current externalities for each period, which could be executed by a planner with full access to the disaggregated state, might fail to achieve the global stability of the social optimum under the same dynamics.