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Journal of Advanced Transportation
Volume 2017, Article ID 5062984, 9 pages
Research Article

Numerical Bounds on the Price of Anarchy

1Industrial Engineering Department, Diego Portales University, Santiago, Chile
2Department of Transport Engineering and Logistics, Pontificia Universidad Católica de Chile, Santiago, Chile

Correspondence should be addressed to Louis de Grange; lc.pdu@egnarged.siuol

Received 7 June 2017; Accepted 27 August 2017; Published 17 October 2017

Academic Editor: Sara Moridpour

Copyright © 2017 Louis de Grange et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Theoretical upper bounds for price of anarchy have been calculated in previous studies. We present an empirical analysis for the price of anarchy for congested transportation networks; different network sizes and demand levels are considered for each network. We obtain a maximum price of anarchy for the cases studied, which is notably lower than the theoretical bounds reported in the literature. This result should be carefully considered in the design and implementation of road pricing mechanisms for cities.