@article{c89147c4901f4f14957cb6c3f7955d34,

title = "When is selfish routing bad? The price of anarchy in light and heavy traffic",

abstract = "This paper examines the behavior of the price of anarchy as a function of the traffic inflow in nonatomic congestion games with multiple origin/destination (O/D) pairs. Empirical studies in real-world networks show that the price of anarchy is close to 1 in both light and heavy traffic, thus raising the following question: can these observations be justified theoretically? We first show that this is not always the case: the price of anarchy may remain a positive distance away from 1 for all values of the traffic inflow, even in simple three-link networks with a single O/D pair and smooth, convex costs. On the other hand, for a large class of cost functions (including all polynomials) and inflow patterns, the price of anarchy does converge to 1 in both heavy and light traffic, irrespective of the network topology and the number of O/D pairs in the network. We also examine the rate of convergence of the price of anarchy, and we show that it follows a power law whose degree can be computed explicitly when the network's cost functions are polynomials.",

keywords = "Heavy traffic, Light traffic, Nonatomic congestion games, Price of anarchy, Regular variation",

author = "Riccardo Colini-Baldeschi and Roberto Cominetti and Panayotis Mertikopoulos and Marco Scarsini",

note = "Funding Information: This research was supported by COST [Action CA16228 {"}European Network for Game Theory{"} (GAMENET)]; the Fondation Math{\'e}matique Jacques Hadamard program PGMOcofunded by EDF, Thales, and Orange [Grant HEAVY.NET]; the National Fund for Scientific and Technological Development of Chile [Grants 1171501 and 1130564]; N{\'u}cleo Milenio [ICM/FIC RC130003 {"}Informaci{\'o}n y Coordinaci{\'o}n en Redes{"}]; ECOS/CONICYT [Grant C15E03]; the Huawei HIRP Flagship project ULTRON; and the Gruppo Nazionale per l'Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni-INdAM project 2019 {"}Markov chains and games on networks.{"} Funding Information: Funding: This research was supported by COST [Action CA16228 “European Network for Game Theory” (GAMENET)]; the Fondation Math{\'e}matique Jacques Hadamard program PGMO cofunded by EDF, Thales, and Orange [Grant HEAVY.NET]; the National Fund for Scientific and Techno-logical Development of Chile [Grants 1171501 and 1130564]; N{\'u}cleo Milenio [ICM/FIC RC130003 “Informaci{\'o}n y Coordinaci{\'o}n en Redes”]; ECOS/CONICYT [Grant C15E03]; the Huawei HIRP Flagship project ULTRON; and the Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni–INdAM project 2019 “Markov chains and games on networks.” Publisher Copyright: {\textcopyright} 2020 INFORMS.",

year = "2020",

month = mar,

doi = "10.1287/opre.2019.1894",

language = "English",

volume = "68",

pages = "411--434",

journal = "Operations Research",

issn = "0030-364X",

publisher = "INFORMS Institute for Operations Research and the Management Sciences",

number = "2",

}