Inefficiency of Nash equilibria
Mathematics of Operations Research
Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the performance of user equilibria in traffic networks
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of selfish behavior in bilateral network formation
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On nash equilibria for a network creation game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the price of anarchy and stability of correlated equilibria of linear congestion games,,
ESA'05 Proceedings of the 13th annual European conference on Algorithms
On the convergence of multicast games in directed networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
On the value of coordination in network design
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Designing networks with good equilibria
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Online multicast with egalitarian cost sharing
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
On Pure and (Approximate) Strong Equilibria of Facility Location Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
$\mathcal{NP}$-Hardness of Pure Nash Equilibrium in Scheduling and Connection Games
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
An O( lognloglogn) upper bound on the price of stability for undirected Shapley network design games
Information Processing Letters
When ignorance helps: Graphical multicast cost sharing games
Theoretical Computer Science
Characterizing the Existence of Potential Functions in Weighted Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Price of Stability in Survivable Network Design
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Competitive cost sharing with economies of scale
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Socially-aware network design games
INFOCOM'10 Proceedings of the 29th conference on Information communications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
A game theoretic analysis of network design with socially-aware users
Computer Networks: The International Journal of Computer and Telecommunications Networking
Strategic multiway cut and multicut games
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
A Nash bargaining solution for cooperative network formation games
NETWORKING'11 Proceedings of the 10th international IFIP TC 6 conference on Networking - Volume Part I
On the price of stability for undirected network design
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
Towards network games with social preferences
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Nash equilibria with minimum potential in undirected broadcast games
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Theoretical Computer Science
Capacitated network design games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Hi-index | 0.00 |
We consider a model of game-theoretic network design initially studied by Anshelevich et al. [2], where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. [2] proved that pure-strategy Nash equilibria always exist and that the price of stability--the ratio in costs of a minimumcost Nash equilibrium and an optimal solution--is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has a weight wi ≥ 1, and its cost share of an edge in its path equals wi times the edge cost, divided by the total weight of the players using the edge.This paper presents the first general results on weighted Shapley network design games. First, we give a simple example with no pure-strategy Nash equilibrium. This motivates considering the price of stability with respect to α-approximate Nash equilibria--outcomes from which no player can decrease its cost by more than an α multiplicative factor. Our first positive result is that O(log wmax)-approximate Nash equilibria exist in all weighted Shapley network design games, where wmax is the maximum player weight. More generally, we establish the following trade-off between the two objectives of good stability and low cost: for every α = Ω(log wmax), the price of stability with respect to O(α)- approximate Nash equilibria is O((log W)/α), where W is the sum of the players' weights. In particular, there is always an O(logW)-approximate Nash equilibrium with cost within a constant factor of optimal.Finally, we show that this trade-off curve is nearly optimal: we construct a family of networks without o(log wmax/ log log wmax)-approximate Nash equilibria, and show that for all α = Ω(logwmax/ log log wmax), achieving a price of stability of O(log W/α) requires relaxing equilibrium constraints by an Ω(α) factor.