An overview of Stackelberg pricing in networks
AbstractThe Stackelberg pricing problem has two levels of decision making: tariff setting by an operator, and then selection of the cheapest alternative by customers. In the network version, an operator determines tariffs on a subset of the arcs that he owns. Customers, who wish to connect two vertices with a path of a certain capacity, select the cheapest path. The revenue for the operator is determined by the tariff and the amount of usage of his arcs. The most natural model for the problem is a (bi-linear) bilevel program, where the upper level problem is the pricing problem of the operator, and the lower level problem is a shortest path problem for each of the customers. This manuscript contains a compilation of theoretical and algorithmic results on the Stackelberg pricing problem. The description of the theory and algorithms is generally informal and intuitive. We redefine the underlying network of the problem, to obtain a compact representation. Then, we describe a basic branch-and-bound enumeration procedure. Both concepts are used for complexity issues and the development of algorithms: establishing NP-hardness, approximability, and polynomially solvable cases, and an efficient exact branch-and-bound algorithm.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 038.
Date of creation: 2005
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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-29 (All new papers)
- NEP-MIC-2005-10-29 (Microeconomics)
- NEP-NET-2005-10-29 (Network Economics)
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- Grigoriev,Alexander & Hoesel,Stan,van & Kraaij,Anton F.,van der & Marc,Uetz & Mustapha,Bouhtou, 2004. "Pricing Network Edges to Cross a River," Research Memoranda 009, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- Martine Labbé & Patrice Marcotte & Gilles Savard, 1998. "A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1608-1622, December.
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