scholarly journals On the Robustness of the Approximate Price of Anarchy in Generalized Congestion Games

2022 ◽  
Author(s):  
Vittorio Bilò
Keyword(s):  
Price Of Anarchy ◽  
Congestion Games

Congestion Games, Load Balancing, and Price of Anarchy

2005 ◽  
pp. 13-27 ◽  
Author(s):  
Anshul Kothari ◽  
Subhash Suri ◽  
Csaba D. Tóth ◽  
Yunhong Zhou
Keyword(s):  
Load Balancing ◽  
Price Of Anarchy ◽  
Congestion Games

scholarly journals Exact Price of Anarchy for Polynomial Congestion Games

2011 ◽  
Vol 40 (5) ◽  
pp. 1211-1233 ◽  
Author(s):  
Sebastian Aland ◽  
Dominic Dumrauf ◽  
Martin Gairing ◽  
Burkhard Monien ◽  
Florian Schoppmann
Keyword(s):  
Price Of Anarchy ◽  
Congestion Games

The sequential price of anarchy for affine congestion games with few players

2019 ◽  
Vol 47 (2) ◽  
pp. 133-139
Author(s):  
Jasper de Jong ◽  
Marc Uetz
Keyword(s):  
Price Of Anarchy ◽  
Congestion Games

scholarly journals The Asymptotic Price of Anarchy for k-uniform Congestion Games

2018 ◽  
pp. 317-328 ◽  
Author(s):  
Jasper de Jong ◽  
Walter Kern ◽  
Berend Steenhuisen ◽  
Marc Uetz
Keyword(s):  
Price Of Anarchy ◽  
Congestion Games

scholarly journals The price of anarchy in routing games as a function of the demand

2021 ◽  
Author(s):  
Roberto Cominetti ◽  
Valerio Dose ◽  
Marco Scarsini
Keyword(s):  
Price Of Anarchy ◽  
Heavy Traffic ◽  
Scaling Law ◽  
Congestion Games ◽  
Social Optimum ◽  
Asymptotic Results ◽  
Worst Case ◽  
Traffic Demand ◽  
Break Points ◽  
Routing Games

AbstractThe 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.

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