Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Group Strategyproof Mechanisms via Primal-Dual Algorithms
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Selfish Routing in Capacitated Networks
Mathematics of Operations Research
The price of selfish behavior in bilateral network formation
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Tight bounds for worst-case equilibria
ACM Transactions on Algorithms (TALG)
Cost-Sharing Mechanisms for Network Design
Algorithmica
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Network Design with Weighted Players
Theory of Computing Systems - Special Issue: Symposium on Parallelism in Algorithms and Architectures 2006; Guest Editors: Robert Kleinberg and Christian Scheideler
The structure and complexity of Nash equilibria for a selfish routing game
Theoretical Computer Science
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
A network creation game with nonuniform interests
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy in network creation games is (mostly) constant
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Near-strong equilibria in network creation games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
The price of anarchy in cooperative network creation games
ACM SIGecom Exchanges
On a bounded budget network creation game
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy in network creation games
ACM Transactions on Algorithms (TALG)
Computer Science Review
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We study a basic network creation game proposed by Fabrikant et al. [2003]. In this game, each player (vertex) can create links (edges) to other players at a cost of α per edge. The goal of every player is to minimize the sum consisting of (a) the cost of the links he has created and (b) the sum of the distances to all other players. Fabrikant et al. conjectured that there exists a constant A such that, for any α A, all nontransient Nash equilibria graphs are trees. They showed that if a Nash equilibrium is a tree, the price of anarchy is constant. In this article, we disprove the tree conjecture. More precisely, we show that for any positive integer n0, there exists a graph built by n ≥ n0 players which contains cycles and forms a nontransient Nash equilibrium, for any α with 1 α ≤ √n/2. Our construction makes use of some interesting results on finite affine planes. On the other hand, we show that, for α ≥ 12n ⌈log n⌉, every Nash equilibrium forms a tree. Without relying on the tree conjecture, Fabrikant et al. proved an upper bound on the price of anarchy of O(√α), where α ∈ [2, n2. We improve this bound. Specifically, we derive a constant upper bound for α ∈ O(√n) and for α ≥ 12n ⌈log n⌉. For the intermediate values, we derive an improved bound of O(1 + (min{α2/n, n2/α})1/3). Additionally, we develop characterizations of Nash equilibria and extend our results to a weighted network creation game as well as to scenarios with cost sharing.