When Efficiency meets Equity in Congestion Pricing and Revenue Refunding Schemes

Congestion pricing has long been hailed as a means to mitigate traffic congestion; however, its practical adoption has been limited due to the resulting social inequity issue, e.g., low-income users are priced out off certain roads. This issue has spurred interest in the design of equitable mechanisms that aim to refund the collected toll revenues as lump-sum transfers to users. Although revenue refunding has been extensively studied for over three decades, there has been no thorough characterization of how such schemes can be designed to simultaneously achieve system efficiency and equity objectives. In this work, we bridge this gap through the study of \emph{congestion pricing and revenue refunding} (CPRR) schemes in non-atomic congestion games. We first develop CPRR schemes, which in comparison to the untolled case, simultaneously increase system efficiency without worsening wealth inequality, while being \emph{user-favorable}: irrespective of their initial wealth or values-of-time (which may differ across users), users would experience a lower travel cost after the implementation of the proposed scheme. We then characterize the set of optimal user-favorable CPRR schemes that simultaneously maximize system efficiency and minimize wealth inequality. Finally, we provide a concrete methodology for computing optimal CPRR schemes and also highlight additional equilibrium properties of these schemes under different models of user behavior. Overall, our work demonstrates that through appropriate refunding policies we can design user-favorable CPRR schemes that maximize system efficiency while reducing wealth inequality.