Computing Nash Equilibria for Scheduling on Restricted Parallel Links
Reads0
Chats0
TLDR
A polynomial time algorithm to compute from any given assignment a Nash equilibrium with non-increased makespan, which results in an improved approximation factor of for identical links, where w1 is the largest user traffic, and to an approximation factors of 2 for related links.Abstract:
We consider the problem of routing n users on m parallel links under the restriction that each user may only be routed on a link from a certain set of allowed links for the user. So, this problem is equivalent to the correspondingly restricted scheduling problem of assigning n jobs to m parallel machines. In a Nash equilibrium, no user may improve its own Individual Cost (latency) by unilaterally switching to another link from its set of allowed links.
For identical links, we present, as our main result, a polynomial time algorithm to compute from any given assignment a Nash equilibrium with non-increased makespan. The algorithm gradually transforms the assignment by pushing the unsplittable user traffics through a flow network, which is constructed from the users and the links. The algorithm uses ideas from blocking flows.
Furthermore, we use techniques simular to those in the generic PreflowPush algorithm to approximate in polynomial time a schedule with optimum makespan. This results to an improved approximation factor of $2-\frac{1}{w_{1}}$for identical links, where w 1 is the largest user traffic, and to an approximation factor of 2 for related links.read more
Citations
More filters
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.
Book ChapterDOI
On the price of anarchy and stability of correlated equilibria of linear congestion games
TL;DR: It is shown that for the sum social cost, which corresponds to the average cost of the players, every linear congestion game has Nash and correlated price of stability at most 1.6, and the same bound holds for symmetric games as well.
Journal ArticleDOI
Coordination mechanisms for selfish scheduling
TL;DR: In this article, the authors study coordination mechanisms for four classes of multiprocessor machine scheduling problems and derive upper and lower bounds on the price of anarchy of these mechanisms, and prove that the system converges to a pure-strategy Nash equilibrium in a linear number of rounds.
Journal ArticleDOI
Approximating Congestion + Dilation in Networks via "Quality of Routing” Games
TL;DR: Nash equilibria of QoR games give poly-log approximations to hard optimization problems in general networks where each player selfishly selects a path that minimizes the sum of congestion and dilation of the player's path.
Journal ArticleDOI
Exact Price of Anarchy for Polynomial Congestion Games
TL;DR: Values for the worst-case price of anarchy in weighted and unweighted (atomic unsplittable) congestion games, provided that all cost functions are bounded-degree polynomials with nonnegative coefficients are shown.
References
More filters
Book
Network Flows: Theory, Algorithms, and Applications
TL;DR: In-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models are presented.
Journal ArticleDOI
Equilibrium points in n-person games
TL;DR: A concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple ofpure strategies, one strategy being taken for each player.
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 ChapterDOI
Worst-case equilibria
TL;DR: In this paper, the authors propose the ratio between the worst possible Nash equilibrium and the social optimum as a measure of the effectiveness of the system and derive upper and lower bounds for this ratio in a model in which several agents share a very simple network.