Uncertainty in Multi-Commodity Routing Networks: When does it help?

TL;DR

This paper investigates how different types of cost perception uncertainties among users affect equilibrium congestion in multi-commodity routing networks, revealing that over-estimation can reduce congestion while under-estimation worsens it.

Contribution

It uncovers the distinct impacts of over- and under-estimation of congestion costs on network equilibria, providing insights for urban transportation policy and dynamic pricing strategies.

Findings

Over-estimation of costs decreases congestion.

Under-estimation of costs increases congestion.

Perception of prices significantly influences policy effectiveness.

Abstract

We study the equilibrium behavior in a multi-commodity selfish routing game with many types of uncertain users where each user over- or under-estimates their congestion costs by a multiplicative factor. Surprisingly, we find that uncertainties in different directions have qualitatively distinct impacts on equilibria. Namely, contrary to the usual notion that uncertainty increases inefficiencies, network congestion actually decreases when users over-estimate their costs. On the other hand, under-estimation of costs leads to increased congestion. We apply these results to urban transportation networks, where drivers have different estimates about the cost of congestion. In light of the dynamic pricing policies aimed at tackling congestion, our results indicate that users' perception of these prices can significantly impact the policy's efficacy, and "caution in the face of uncertainty" leads to favorable network conditions.