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Author Colini-Baldeschi, R.; Cominetti, R.; Scarsini, M.
Title Price of Anarchy for Highly Congested Routing Games in Parallel Networks Type
Year 2019 Publication Theory Of Computing Systems Abbreviated Journal Theor. Comput. Syst.
Volume 63 Issue 1 Pages 90-113
Keywords Nonatomic routing games; Price of Anarchy; Regularly varying functions; Wardrop equilibrium; Parallel networks; High congestion
Abstract We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.
Address [Colini-Baldeschi, Riccardo; Scarsini, Marco] LUISS, Dipartimento Econ & Finanza, Viale Romania 32, I-00197 Rome, Italy, Email: rcolini@luiss.it;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1432-4350 ISBN Medium
Area Expedition Conference
Notes WOS:000456320200005 Approved
Call Number UAI @ eduardo.moreno @ Serial 974
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Author Cominetti, R.; Dose, V.; Scarsini, M.
Title The price of anarchy in routing games as a function of the demand Type
Year 2022 Publication Mathematical Programming Abbreviated Journal Math. Program.
Volume Early Access Issue Pages
Keywords Nonatomic routing games; Price of anarchy; Affine cost functions; Variable demand
Abstract The price of anarchy has become a standard measure of the efficiency of equilibria in games. Most of the literature in this area has focused on establishing worst-case bounds for specific classes of games, such as routing games or more general congestion games. Recently, the price of anarchy in routing games has been studied as a function of the traffic demand, providing asymptotic results in light and heavy traffic. The aim of this paper is to study the price of anarchy in nonatomic routing games in the intermediate region of the demand. To achieve this goal, we begin by establishing some smoothness properties of Wardrop equilibria and social optima for general smooth costs. In the case of affine costs we show that the equilibrium is piecewise linear, with break points at the demand levels at which the set of active paths changes. We prove that the number of such break points is finite, although it can be exponential in the size of the network. Exploiting a scaling law between the equilibrium and the social optimum, we derive a similar behavior for the optimal flows. We then prove that in any interval between break points the price of anarchy is smooth and it is either monotone (decreasing or increasing) over the full interval, or it decreases up to a certain minimum point in the interior of the interval and increases afterwards. We deduce that for affine costs the maximum of the price of anarchy can only occur at the break points. For general costs we provide counterexamples showing that the set of break points is not always finite.
Address
Corporate Author Thesis
Publisher Place of Publication Editor
Language Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0025-5610 ISBN Medium
Area Expedition Conference
Notes WOS:000693858200001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1468
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