Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
How much can taxes help selfish routing?
Proceedings of the 4th ACM conference on Electronic commerce
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Edge Pricing of Multicommodity Networks for Heterogeneous Selfish Users
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Tolls for Heterogeneous Selfish Users in Multicommodity Networks and Generalized Congestion Games
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
Linear tolls suffice: new bounds and algorithms for tolls in single source networks
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Taxes for linear atomic congestion games
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
The effectiveness of Stackelberg strategies and tolls for network congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Nash equilibria, the price of anarchy and the fully mixed nash equilibrium conjecture
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Improving the Efficiency of Load Balancing Games through Taxes
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Efficient Methods for Selfish Network Design
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Uplink power control and base station association in multichannel cellular networks
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Taxes for linear atomic congestion games
ACM Transactions on Algorithms (TALG)
The impact of altruism on the efficiency of atomic congestion games
TGC'10 Proceedings of the 5th international conference on Trustworthly global computing
Efficient methods for selfish network design
Theoretical Computer Science
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We investigate the existence of optimal tolls for atomic symmetric network congestion games with unsplittable traffic and arbitrary non-negative and non-decreasing latency functions. We focus on pure Nash equilibria and a natural toll mechanism, which we call cost-balancing tolls. A set of cost-balancing tolls turns every path with positive traffic on its edges into a minimum cost path. Hence any given configuration is induced as a pure Nash equilibrium of the modified game with the corresponding cost-balancing tolls. We show how to compute in linear time a set of cost-balancing tolls for the optimal solution such that the total amount of tolls paid by any player in any pure Nash equilibrium of the modified game does not exceed the latency on the maximum latency path in the optimal solution. Our main result is that for congestion games on series-parallel networks with increasing latencies, the optimal solution is induced as the unique pure Nash equilibrium of the game with the corresponding cost-balancing tolls. To the best of our knowledge, only linear congestion games on parallel links were known to admit optimal tolls prior to this work. To demonstrate the difficulty of computing a better set of optimal tolls, we show that even for 2-player linear congestion games on series-parallel networks, it is NP-hard to decide whether the optimal solution is the unique pure Nash equilibrium or there is another equilibrium of total cost at least 6/5 times the optimal cost.