Open Access
Approximate Equilibria and Ball Fusion.
Elias Koutsoupias,Marios Mavronicolas,Paul G. Spirakis +2 more
- pp 223-235
TLDR
In this paper, the authors consider selfish routing over a network consisting of m parallel bottleneck links through which $n$ selfish users route their traffic trying to minimize their own expected latency.Abstract:
We consider selfish routing over a network consisting of m parallel
links through which $n$ selfish users route their traffic trying to
minimize their own expected latency. We study the class of mixed
strategies in which the expected latency through each link is at most
a constant multiple of the optimum maximum latency had global
regulation been available. For the case of uniform links it is known
that all Nash equilibria belong to this class of strategies. We are
interested in bounding the coordination ratio (or price of anarchy) of
these strategies defined as the worst-case ratio of the maximum (over
all links) expected latency over the optimum maximum latency. The load
balancing aspect of the problem immediately implies a lower bound
Ω(ln m ln ln m) of the coordination
ratio. We give a tight (up to a multiplicative constant) upper bound.
To show the upper bound, we analyze a variant of the classical balls
and bins problem, in which balls with arbitrary weights are placed
into bins according to arbitrary probability distributions. At the
heart of our approach is a new probabilistic tool that we call ball
fusion; this tool is used to reduce the variant of the problem where
balls bear weights to the classical version (with no weights). Ball
fusion applies to more general settings such as links with arbitrary
capacities and other latency functions.read more
Citations
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Proceedings ArticleDOI
The price of anarchy of finite congestion games
TL;DR: The price of anarchy of pure Nash equilibria in congestion games with linear latency functions is considered and some of the results are extended to latency functions that are polynomials of bounded degree.
Proceedings ArticleDOI
Intrinsic robustness of the price of anarchy
TL;DR: This work proves a general and fundamental connection between the price of anarchy and its seemingly stronger relatives in classes of games with a sum objective, and identifies classes ofgames that are tight, in the sense that smoothness arguments are guaranteed to produce an optimal worst-case upper bound on the POA, even for the smallest set of interest (pure Nash equilibria).
Proceedings ArticleDOI
Tight bounds for worst-case equilibria
Artur Czumaj,Berthold Vöcking +1 more
TL;DR: In this article, the worst-case coordination ratio on m parallel links was shown to be Θ(log m/log log log log m) where m is the number of parallel links.
Book ChapterDOI
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
Dimitris Fotakis,Spyros Kontogiannis,Elias Koutsoupias,Elias Koutsoupias,Marios Mavronicolas,Paul G. Spirakis,Paul G. Spirakis +6 more
TL;DR: This work provides a comprehensive collection of efficient algorithms, hardness results (both as NP-hardness and #P-completeness results), and structural results for these algorithmic problems related to the computation of Nash equilibria for the selfish routing game the authors consider.
Journal ArticleDOI
Selfish unsplittable flows
TL;DR: It is proved that any weighted network congestion game with linear edge delays admits a pure Nash equilibrium that can be found in pseudo-polynomial time.
References
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Book
Theory of Games and Economic Behavior
TL;DR: Theory of games and economic behavior as mentioned in this paper is the classic work upon which modern-day game theory is based, and it has been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations.
Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Book
A Course in Game Theory
TL;DR: A Course in Game Theory as discussed by the authors presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts.
Book ChapterDOI
Non-cooperative games
TL;DR: In this article, it was shown that the set of equilibrium points of a two-person zero-sum game can be defined as a set of all pairs of opposing "good" strategies.
Book
Randomized Algorithms
TL;DR: This book introduces the basic concepts in the design and analysis of randomized algorithms and presents basic tools such as probability theory and probabilistic analysis that are frequently used in algorithmic applications.