A bilevel model of taxation and its application to optimal highway pricing
Management Science
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
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
Buying cheap is expensive: hardness of non-parametric multi-product pricing
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Aspects of a 2-Player Stackelberg Shortest Paths Tree Game
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Specializations and generalizations of the stackelberg minimum spanning tree game
WINE'10 Proceedings of the 6th international conference on Internet and network economics
New formulations and valid inequalities for a bilevel pricing problem
Operations Research Letters
An exact algorithm for the network pricing problem
Discrete Optimization
Valid inequalities and branch-and-cut for the clique pricing problem
Discrete Optimization
The stackelberg minimum spanning tree game
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs
Journal of Combinatorial Optimization
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We consider a Stackelberg pricing problem in directed networks. Tariffs have to be defined by an operator, the leader, for a subset of the arcs, the tariff arcs. Clients, the followers, choose paths to route their demand through the network selfishly and independently of each other, on the basis of minimal cost. Assuming there exist bounds on the costs clients are willing to bear, the problem is to find tariffs such as to maximize the operator's revenue. Except for the case of a single client, no approximation algorithm is known to date for that problem. We derive the first approximation algorithms for the case of multiple clients. Our results hold for a restricted version of the problem where each client takes at most one tariff arc to route the demand. We prove that this problem is still strongly ${\mathcal NP}$-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + ln D)–approximation. Here, m is the number of tariff arcs, and D is upper bounded by the total demand. We furthermore derive lower and upper bounds for the approximability of the pricing problem where the operator must serve all clients, and we discuss some polynomial special cases. A computational study with instances from France Télécom suggests that uniform pricing performs better than theory would suggest.