Some analytical results on spatial price differentiation in first–best congestion pricing schemes

In this study, we examine a class of first–best congestion pricing schemes that employ various strategies to differentiate price spatially. Since spatial price differentiation raises the issue of privacy infringement, two hybrid pricing schemes are proposed to internalize travelers’ privacy cost. Under these schemes, a traveler is given the options to maintain her anonymity and pay a “regular” toll, or compromise her privacy and receive a discount. One of the hybrid schemes allows the traveler's privacy cost to be dependent on the link composition of the traveler's path. In other words, she can choose to disclose none, part, or all of her path information. We prove that the minimum toll burden—with or without the privacy cost—required to decentralize a system optimum gradually decreases as the toll becomes more spatially differentiated. We also show that the new hybrid scheme demonstrates some interesting analytical properties compared to existing schemes.