Journal of the ACM (JACM)
Pricing network edges for heterogeneous selfish users
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The price of anarchy is independent of the network topology
Journal of Computer and System Sciences - STOC 2002
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)
How much can taxes help selfish routing?
Journal of Computer and System Sciences - Special issue on network algorithms 2005
On the severity of Braess's paradox: designing networks for selfish users is hard
Journal of Computer and System Sciences - Special issue on FOCS 2001
The effectiveness of Stackelberg strategies and tolls for network congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Stackelberg Strategies and Collusion in Network Games with Splittable Flow
Approximation and Online Algorithms
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Stackelberg Routing in Arbitrary Networks
Mathematics of Operations Research
Improving the price of anarchy for selfish routing via coordination mechanisms
ESA'11 Proceedings of the 19th European conference on Algorithms
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An effective means to reduce the inefficiency of Nash flows in nonatomic network routing games is to impose tolls on the arcs of the network. It is a well-known fact that marginal cost tolls induce a Nash flow that corresponds to a minimum cost flow. However, despite their effectiveness, marginal cost tolls suffer from two major drawbacks, namely (i) that potentially every arc of the network is tolled, and (ii) that the imposed tolls can be arbitrarily large. In this paper, we study the restricted network toll problem in which tolls can be imposed on the arcs of the network but are restricted to not exceed a predefined threshold for every arc. We show that optimal restricted tolls can be computed efficiently for parallel-arc networks and affine latency functions. This generalizes a previous work on taxing subnetworks to arbitrary restrictions. Our algorithm is quite simple, but relies on solving several convex programs. The key to our approach is a characterization of the flows that are inducible by restricted tolls for single-commodity networks. We also derive bounds on the efficiency of restricted tolls for multi-commodity networks and polynomial latency functions. These bounds are tight even for parallel-arc networks. Our bounds show that restricted tolls can significantly reduce the price of anarchy if the restrictions imposed on arcs with high-degree polynomials are not too severe. Our proof is constructive. We define tolls respecting the given thresholds and show that these tolls lead to a reduced price of anarchy by using a (λ,µ)-smoothness approach.