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Author (up) Colini-Baldeschi, R.; Cominetti, R.; Mertikopoulos, P.; Scarsini, M.
Title When Is Selfish Routing Bad? The Price of Anarchy in Light and Heavy Traffic Type
Year 2020 Publication Operations Research Abbreviated Journal Oper. Res.
Volume 68 Issue 2 Pages 411-434
Keywords nonatomic congestion games; price of anarchy; light traffic; heavy traffic; regular variation
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.
Address [Colini-Baldeschi, Riccardo] Facebook Inc, Core Data Sci Grp, London W1T 1FB, England, Email: rickuz@fb.com;
Corporate Author Thesis
Publisher Informs Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0030-364x ISBN Medium
Area Expedition Conference
Notes WOS:000521730200006 Approved
Call Number UAI @ eduardo.moreno @ Serial 1128
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Author (up) 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 (up) 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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Author (up) Cominetti, R.; Quattropani, M.; Scarsini, M.
Title The Buck-Passing Game Type
Year 2022 Publication Mathematics Operations Research Abbreviated Journal Math. Oper. Res.
Volume Early Access Issue Pages
Keywords prior-free equilibrium; generalized ordinal potential game; finite improvement property; fairness of equilibria; price of anarchy; price of stability; Markov chain tree theorem; PageRank; PageRank game
Abstract We consider two classes of games in which players are the vertices of a directed graph. Initially, nature chooses one player according to some fixed distribution and gives the player a buck. This player passes the buck to one of the player's out-neighbors in the graph. The procedure is repeated indefinitely. In one class of games, each player wants to minimize the asymptotic expected frequency of times that the player receives the buck. In the other class of games, the player wants to maximize it. The PageRank game is a particular case of these maximizing games. We consider deterministic and stochastic versions of the game, depending on how players select the neighbor to which to pass the buck. In both cases, we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. If the graph on which the game is played admits a Hamiltonian cycle, then this is the outcome of prior-five Nash equilibrium in the minimizing game. For the minimizing game, we then use the price of anarchy and stability to measure fairness of these equilibria.
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 0364-765X ISBN Medium
Area Expedition Conference
Notes WOS:000731930100001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1502
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Author (up) Cominetti, R.; Scarsini, M.; Schroder, M.; Stier-Moses, N.
Title Approximation and Convergence of Large Atomic Congestion Games Type
Year 2022 Publication Mathematics of Operations Research Abbreviated Journal Math. Oper. Res.
Volume Early Access Issue Pages
Keywords unsplittable atomic congestion games; nonatomic congestion games; Wardrop equilibrium; Poisson games; symmetric equilibrium; price of anarchy; price of stability; total variation
Abstract We consider the question of whether and in what sense, Wardrop equilibria provide a good approximation for Nash equilibria in atomic unsplittable congestion games with a large number of small players. We examine two different definitions of small players. In the first setting, we consider games in which each player's weight is small. We prove that when the number of players goes to infinity and their weights to zero, the random flows in all (mixed) Nash equilibria for the finite games converge in distribution to the set of Wardrop equilibria of the corresponding nonatomic limit game. In the second setting, we consider an increasing number of players with a unit weight that participate in the game with a decreasingly small probability. In this case, the Nash equilibrium flows converge in total variation toward Poisson random variables whose expected values are War drop equilibria of a different nonatomic game with suitably defined costs. The latter can be viewed as symmetric equilibria in a Poisson game in the sense of Myerson, establishing a plausible connection between the Wardrop model for routing games and the stochastic fluctuations observed in real traffic. In both settings, we provide explicit approximation bounds, and we study the convergence of the price of anarchy. Beyond the case of congestion games, we prove a general result on the convergence of large games with random players toward Poisson games.
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 0364-765X ISBN Medium
Area Expedition Conference
Notes WOS:000850694300001 Approved
Call Number UAI @ alexi.delcanto @ Serial 1647
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