# 15-045/VIII (2015-03-31)

Erik T. Verhoef, VU University Amsterdam, the Netherlands; Hugo E. Silva, VU University Amsterdam, the Netherlands
Congestion pricing, dynamic congestion, market power, internalization
JEL codes:
R41, R48, D62

Various contributions to the recent literature on congestion pricing have demonstrated that when services at a congestible facility are provided by operators with market power, the case in point often being a few airlines jointly using a congested airport, optimal congestion pricing rules deviate from the familiar Pigouvian rule that tolls be equal to the marginal external costs. The reason is that an operator with market power has an incentive to internalize the congestion effects that its customers and vehicles impose upon one-another, so that Pigouvian tolling would lead to overpricing of congestion. More recent contributions to this literature, however, have brought to the fore that when congestion at the facility takes on the form of dynamic bottleneck congestion à la Vickrey (1969), where trip scheduling is the key behavioural margin, there may exist no Nash e quilibrium in arrival schedules for oligopolistic operators also under rather plausible assumptions on parameters. This paper investigates whether in such cases, an equilibrium does exist for another congestion technology, namely the Henderson-Chu dynamic model of flow congestion. We find that a stable and unique equilibrium exists also in cases where it fails to exist under bottleneck congestion (notably when the value of schedule late exceeds the value of travel delays). Our results suggest that self-internalization with only two firms leads to a considerable efficiency gain compared to the atomistic equilibrium (83% or more of the gain from first-best pricing in our numerical exercises).