Data structures and network algorithms
Data structures and network algorithms
The mathematics of nonlinear programming
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Exponential lower bounds for finding Brouwer fixed points
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Network flows: theory, algorithms, and applications
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Generic Uniqueness of Equilibrium in Large Crowding Games
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How much can taxes help selfish routing?
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Pricing congestible network resources
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How much can taxes help selfish routing?
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How to route and tax selfish unsplittable traffic
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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
Tradeoffs in worst-case equilibria
Theoretical Computer Science - Approximation and online algorithms
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
Designing networks with good equilibria
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Bertrand Competition in Networks
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Improving the Efficiency of Load Balancing Games through Taxes
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Theoretical Computer Science
The Impact of Oligopolistic Competition in Networks
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Cost-balancing tolls for atomic network congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Priority based load balancing in a self-interested P2P network
DBISP2P'05/06 Proceedings of the 2005/2006 international conference on Databases, information systems, and peer-to-peer computing
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Designing Network Protocols for Good Equilibria
SIAM Journal on Computing
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ESA'11 Proceedings of the 19th European conference on Algorithms
Efficiency of restricted tolls in non-atomic network routing games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Discrete Fixed Points: Models, Complexities, and Applications
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Fast Convergence to Wardrop Equilibria by Adaptive Sampling Methods
SIAM Journal on Computing
The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games
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Pricing network edges to cross a river
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The efficiency of optimal taxes
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Operations Research Letters
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ACM Transactions on Algorithms (TALG)
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WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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We study the negative consequences of selfish behavior in a congested network and economic means of influencing such behavior. We consider a model of selfish routing in which the latency experienced by network traffic on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route traffic on minimum-latency paths. The quality of a routing of traffic is measured by the sum of travel times (the total latency).It is well known that the outcome of selfish routing (a Nash equilibrium) does not minimize the total latency. An ancient strategy for improving the selfish solution is the principle of marginal cost pricing, which asserts that on each edge of the network, each network user on the edge should pay a tax offsetting the congestion effects caused by its presence. By pricing network edges according to this principle, the inefficiency of selfish routing can always be eradicated.This result, while fundamental, assumes a very strong homogeneity property: all network users are assumed to trade off time and money in an identical way. The guarantee also ignores both the algorithmic aspects of edge pricing and the unfortunate possibility that an efficient routing of traffic might only be achieved with exorbitant taxes. Motivated by these shortcomings, we extend this classical work on edge pricing in several different directions and prove the following results.We prove that the edges of a single-commodity network can always be priced so that an optimal routing of traffic arises as a Nash equilibrium, even for very general heterogeneous populations of network users.When there are only finitely many different types of network users and all edge latency functions are convex, we show how to compute such edge prices efficiently.We prove that an easy-to-check mathematical condition on the population of heterogeneous network users is both necessary and sufficient for the existence of edge prices that induce an optimal routing while requiring only moderate taxes.