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

See all articles by Hugo Silva

Hugo Silva

VU University Amsterdam; Tinbergen Institute

Robin Lindsey

University of British Columbia (UBC) - Sauder School of Business

André de Palma

Ecole Normale Supérieure de Cachan

Vincent A.C. van den Berg

VU University Amsterdam; Tinbergen Institute

Date Written: July 1, 2014

Abstract

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

Silva, Hugo and Lindsey, Charles Robin and de Palma, André and van den Berg, Vincent A.C., On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users (July 1, 2014). Tinbergen Institute Discussion Paper 14-077/VIII, Available at SSRN: https://ssrn.com/abstract=2461180 or http://dx.doi.org/10.2139/ssrn.2461180

Hugo Silva (Contact Author)

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Charles Robin Lindsey

University of British Columbia (UBC) - Sauder School of Business ( email )

2053 Main Mall
Vancouver, BC V6T 1Z2
Canada

André De Palma

Ecole Normale Supérieure de Cachan ( email )

61 Avenue du President Wilson
94235 Cachan
France
33688714344 (Phone)

Vincent A.C. van den Berg

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

HOME PAGE: http://www.feweb.vu.nl/nl/afdelingen-en-instituten/spatial-economics/staff/v-berg/index.asp

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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