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An overview of Stackelberg pricing in networks

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  • van Hoesel, C.P.M.

    (Quantitative Economics)

Abstract

The 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 (bilinear) 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 paper contains a compilation of theoretical and algorithmic results on the network 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 for the development of algorithms: establishing NP-hardness, approximability, special cases solvable in polynomial time, and an efficient exact branch-and-bound algorithm.

Suggested Citation

  • van Hoesel, C.P.M., 2006. "An overview of Stackelberg pricing in networks," Research Memorandum 043, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2006043
    DOI: 10.26481/umamet.2006043
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Jean Cardinal & Erik D. Demaine & Samuel Fiorini & Gwenaël Joret & Ilan Newman & Oren Weimann, 2013. "The Stackelberg minimum spanning tree game on planar and bounded-treewidth graphs," Journal of Combinatorial Optimization, Springer, vol. 25(1), pages 19-46, January.

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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