Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The price of anarchy is independent of the network topology
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth 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
Selfish routing
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 selfish behavior in bilateral network formation
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
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
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
The Price of Anarchy of a Network Creation Game with Exponential Payoff
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Improved equilibria via public service advertising
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Network Creation Games with Disconnected Equilibria
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Large human communication networks: patterns and a utility-driven generator
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Who should pay for forwarding packets?
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
Brief announcement: the price of anarchy for distributed network formation in an adversary model
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Analysis of large multi-modal social networks: patterns and a generator
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
The price of anarchy in network creation games is (mostly) constant
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
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
A game theoretic framework for peer-to-peer market economy
International Journal of Grid and Utility Computing
On dynamics in basic network creation games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Minimizing the diameter of a network using shortcut edges
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Towards network games with social preferences
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Selfish overlay network creation and maintenance
IEEE/ACM Transactions on Networking (TON)
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
Asymmetric swap-equilibrium: a unifying equilibrium concept for network creation games
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
ACM SIGMETRICS Performance Evaluation Review
Basic network creation games with communication interests
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Bounded-Distance network creation games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
The max-distance network creation game on general host graphs
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Naturality of Network Creation Games, Measurement and Analysis
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
On the structure of equilibria in basic network formation
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We study Nash equilibria in the setting of network creation games introduced recently by Fabrikant, Luthra, Maneva, Papadimitriou and Shenker. In this game we have a set of selfish node players, each creating some incident links, and the goal is to minimize α times the cost of the created links plus sum of the distances to all other players. Fabrikant et al. proved an upper bound O(√α) on the price of anarchy, i.e., the relative cost of the lack of coordination. Albers, Eilts, Even-Dar, Mansour, and Roditty show that the price of anarchy is constant for α = O(√n) and for α ≥ 12n[lg n], and that the price of anarchy is 15(1+min {α2n, n2α})1/3) for any α. The latter bound shows the first sublinear worst-case bound, O(n1/3), for all α. But no better bound is known for α between ω(√n) and o(n lg n). Yet α ≈ n is perhaps the most interesting range, for it corresponds to considering the average distance (instead ofthe sum of distances) to other nodes to be roughly on par with link creation (effectively dividing α by n). In this paper, we prove the first o(nε) upper bound for general α, namely 2O(√lg n). We also prove aconstant upper bound for α = O(n1-ε) for any fixed ε 0, substantially reducing the range of α for which constant bounds have not been obtained. Along the way, we also improve the constant upper bound by Albers et al. (with the leadconstant of 15 ) to 6 for α n/2)1/2 and to 4 for α n/2)1/3}. Next we consider the bilateral network variant of Corbo and Parkesin which links can be created only with the consent of both end points and the link price is shared equally by the two. Corbo and Parkes show an upper bound of O(√α) and a lower bound of Ω(lg α) for α ≤ n. In this paper, we show that in fact the upper bound O(√α) is tight for α ≤, by proving a matching lower bound of Ω(√α). For α n, we prove that the price of anarchy is Θ(n/√ α). Finally we introduce a variant of both network creation games, in which each player desires to minimize α times the cost of its created links plus the maximum distance (instead of the sum of distances) to the other players. This variant of the problem is naturally motivated by considering the worst case instead of the average case. Interestingly, for the original (unilateral) game, we show that the price of anarchy is at most 2 for α ≥ n, O(min{4√lg n, (n/α)1/3}) for 2√lgn ≤ α ≤ n, and O(n2/α) for α n. For the bilateral game, we prove matching upper and lower bounds of Θ(nα+1) for α ≤ n, and an upper bound of 2 for α n.