scholarly journals Atomic congestion games with random players: network equilibrium and the price of anarchy

2020 ◽  
Author(s):  
Chenlan Wang ◽  
Xuan Vinh Doan ◽  
Bo Chen
Keyword(s):  
Price Of Anarchy ◽  
Congestion Games ◽  
Network Equilibrium

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.

scholarly journals Optimal Taxes in Atomic Congestion Games

2021 ◽  
Vol 9 (3) ◽  
pp. 1-33
Author(s):  
Dario Paccagnan ◽  
Rahul Chandan ◽  
Bryce L. Ferguson ◽  
Jason R. Marden
Keyword(s):  
Marginal Cost ◽  
Price Of Anarchy ◽  
Local Information ◽  
Congestion Games ◽  
Shared Resources ◽  
Lower Efficiency ◽  
Traffic Routing ◽  
Linear Programming Formulation ◽  
Correlated Equilibria ◽  
Optimal Taxes

How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing. Within this context, a methodology for designing tolling mechanisms that minimize the system inefficiency (price of anarchy) exploiting solely local information is so far missing in spite of the scientific interest. In this article, we resolve this problem through a tractable linear programming formulation that applies to and beyond polynomial congestion games. When specializing our approach to the polynomial case, we obtain tight values for the optimal price of anarchy and corresponding tolls, uncovering an unexpected link with load balancing games. We also derive optimal tolling mechanisms that are constant with the congestion level, generalizing the results of Caragiannis et al. [8] to polynomial congestion games and beyond. Finally, we apply our techniques to compute the efficiency of the marginal cost mechanism. Surprisingly, optimal tolling mechanism using only local information perform closely to existing mechanism that utilize global information, e.g., Bilò and Vinci [6], while the marginal cost mechanism, known to be optimal in the continuous-flow model, has lower efficiency than that encountered levying no toll. All results are tight for pure Nash equilibria and extend to coarse correlated equilibria.

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