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Title: Price of anarchy is maximized at the percolation threshold

Abstract

When many independent users try to route traffic through a network, the flow can easily become suboptimal as a consequence of congestion of the most efficient paths. The degree of this suboptimality is quantified by the so-called \price of anarchy" (POA), but so far there are no general rules for when to expect a large POA in a random network. Here I address this question by introducing a simple model of flow through a network with randomly-placed "congestible" and "incongestible" links. I show that the POA is maximized precisely when the fraction of congestible links matches the percolation threshold of the lattice. Further, for large networks the value of the POA appears to saturate at its theoretical maximum value.

Authors:
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division
OSTI Identifier:
1395037
DOE Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 91; Journal Issue: 5; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Skinner, Brian. Price of anarchy is maximized at the percolation threshold. United States: N. p., 2015. Web. doi:10.1103/PhysRevE.91.052126.
Skinner, Brian. Price of anarchy is maximized at the percolation threshold. United States. doi:10.1103/PhysRevE.91.052126.
Skinner, Brian. Fri . "Price of anarchy is maximized at the percolation threshold". United States. doi:10.1103/PhysRevE.91.052126.
@article{osti_1395037,
title = {Price of anarchy is maximized at the percolation threshold},
author = {Skinner, Brian},
abstractNote = {When many independent users try to route traffic through a network, the flow can easily become suboptimal as a consequence of congestion of the most efficient paths. The degree of this suboptimality is quantified by the so-called \price of anarchy" (POA), but so far there are no general rules for when to expect a large POA in a random network. Here I address this question by introducing a simple model of flow through a network with randomly-placed "congestible" and "incongestible" links. I show that the POA is maximized precisely when the fraction of congestible links matches the percolation threshold of the lattice. Further, for large networks the value of the POA appears to saturate at its theoretical maximum value.},
doi = {10.1103/PhysRevE.91.052126},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
issn = {1539-3755},
number = 5,
volume = 91,
place = {United States},
year = {2015},
month = {5}
}

Works referenced in this record:

Percolation, quantum tunnelling and the integer Hall effect
journal, May 1988


Price of Anarchy in Transportation Networks: Efficiency and Optimality Control
journal, September 2008