When Efficiency meets Equity in Congestion Pricing and Revenue Refunding Schemes

Abstract

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 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 (i) increase system efficiency and (ii) decrease wealth inequality, while being (iii) 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. These results assume a well-studied behavior model of users minimizing a linear function of their travel times and tolls, without considering refunds. We also study a more complex behavior model wherein users are influenced by and react to the amount of refund that they receive. Although, in general, the two models can result in different outcomes in terms of system efficiency and wealth inequality, we establish that those outcomes coincide when the aforementioned optimal CPRR scheme is implemented. Overall, our work demonstrates that through appropriate refunding policies we can achieve system efficiency while reducing wealth inequality.

When Efficiency Meets Equity in Congestion Pricing and Revenue Refunding Schemes

“…The above properties are well defined for any wealth inequality distribution when the incomes of all users are strictly positive, which we assume in this work. We note that the above properties are fairly natural [10,16] and hold for commonly used wealth-inequality measures, such as the discrete Gini coefficient, which we elucidate in detail in the online version of our paper [22]. Furthermore, we note that the above properties jointly imply an important property of the wealthinequality measureW , which we elucidate in detail in Appendix A.1.…”

“…We refer the readers to the extended version of this paper [22] for a more detailed description of the above properties. The above properties are well defined for any wealth inequality distribution when the incomes of all users are strictly positive, which we assume in this work.…”

“…In the extended version of this paper [22], we also consider the important special case of travel demand when users travel between the same O-D pair, and have values-of-time that are in proportion to their income. In this setting, we establish the existence of a Pareto improving CPRR scheme that results in an ex-post income distribution that has a lower wealth inequality as compared to that of the ex-ante income distribution, which is a stronger result than the more general case with multiple O-D pairs considered above.…”

“…We reiterate that the above notion of an exogenous equilibrium is the standard Nash equilibrium concept used in non-atomic congestion games. In this work, we refer to this equilibrium concept as exogenous to explicitly distinguish it from the endogenous setting when coalitions of users also account for refunds when making travel decisions (see the extended version of this paper [22] for more details on the endogenous setting). A key property of any exogenous τ -equilibrium f is that all users within a given group д ∈ G incur the same travel cost without refunds, irrespective of the path on which they travel.…”

“…In the extended version of our paper [22] we also study CPRR schemes in the context of endogenous equilibria, wherein users also consider refunds in their travel cost minimization. Our work demonstrates that if we utilize the collected toll revenues to devise appropriate refunding policies then we can achieve system efficiency whilst also progressing towards reduced inequality.…”