Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Journal of the ACM (JACM)
Introductory Discrete Mathematics
Introductory Discrete Mathematics
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Topological Conditions for Uniqueness of Equilibrium in Networks
Mathematics of Operations Research
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
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Algorithms for pure Nash equilibria in weighted congestion games
Journal of Experimental Algorithmics (JEA)
Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users
Mathematics of Operations Research
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Equilibria of atomic flow games are not unique
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Pure Nash equilibria in player-specific and weighted congestion games
Theoretical Computer Science
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of 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
Fast and compact: a simple class of congestion games
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
On the complexity of pure Nash equilibria in player-specific network congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
On the existence of pure nash equilibria inweighted congestion games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Weighted congestion games: price of anarchy, universal worst-case examples, and tightness
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part II
Characterizing the Existence of Potential Functions in Weighted Congestion Games
Theory of Computing Systems - Special Issue: Algorithmic Game Theory
Strong and correlated strong equilibria in monotone congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
The equilibrium existence problem in finite network congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Exact price of anarchy for polynomial congestion games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Routing (un-) splittable flow in games with player-specific linear latency functions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Atomic congestion games among coalitions
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Optimal Cost Sharing for Resource Selection Games
Mathematics of Operations Research
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We study the existence of pure Nash equilibria in weighted congestion games. Let C denote a set of cost functions. We say that C is consistent if every weighted congestion game with cost functions in C possesses a pure Nash equilibrium. Our main contribution is a complete characterization of consistency of continuous cost functions. We prove that a set C of continuous functions is consistent for two-player games if and only if C contains only monotonic functions and for all nonconstant functions c1, c2 ∈ C, there are constants a, b ∈ R such that c1(x) = a c2(x) + b for all x ∈ R≥0. For games with at least three players, we prove that C is consistent if and only if exactly one of the following cases holds: (a) C contains only affine functions; (b) C contains only exponential functions such that c(x) = ac eφx + bc for some ac, bc, φ ∈ R, where ac and bc may depend on c, while φ must be equal for every c ∈ C. The latter characterization is even valid for three-player games. Finally, we derive several characterizations of consistency of cost functions for games with restricted strategy spaces, such as weighted network congestion games or weighted congestion games with singleton strategies.