On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users
Tinbergen Institute Discussion Paper 14-077/VIII
43 Pages Posted: 4 Jul 2014
Date Written: July 1, 2014
This paper investigates the existence and uniqueness of equilibrium in the Vickrey bottleneck model when each user controls a positive fraction of total traffic. Users simultaneously choose departure schedules for their vehicle fleets. Each user internalizes the congestion cost that each of its vehicles imposes on other vehicles in its fleet. We establish three results. First, a pure strategy Nash equilibrium (PSNE) may not exist. Second, if a PSNE does exist, identical users may incur appreciably different equilibrium costs. Finally, a multiplicity of PSNE can exist in which no queuing occurs but departures begin earlier or later than in the social optimum. The order in which users depart can be suboptimal as well. Nevertheless, by internalizing self-imposed congestion costs individual users can realize much, and possibly all, of the potential cost savings from either centralized traffic control or time-varying congestion tolls.
Keywords: Bottleneck model, Large users, Atomic users, Existence of Equilibrium, Uniqueness of Equilibrium
JEL Classification: L09, R04, C07
Suggested Citation: Suggested Citation