IDEAS home Printed from https://ideas.repec.org/p/unm/umamet/2006043.html
   My bibliography  Save this paper

An overview of Stackelberg pricing in networks

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://cris.maastrichtuniversity.nl/ws/files/51481414/RM06043.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.26481/umamet.2006043?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Grigoriev, A. & van Hoesel, C.P.M. & van der Kraaij, A.F. & Uetz, M.J. & Bouhtou, M., 2004. "Pricing network edges to cross a river," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    2. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    3. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    4. Ke, Ginger Y. & Zhang, Huiwen & Bookbinder, James H., 2020. "A dual toll policy for maintaining risk equity in hazardous materials transportation with fuzzy incident rate," International Journal of Production Economics, Elsevier, vol. 227(C).
    5. S. Dempe & J. F. Bard, 2001. "Bundle Trust-Region Algorithm for Bilinear Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 265-288, August.
    6. Huang, Wentao & Jian, Sisi & Rey, David, 2024. "Non-additive network pricing with non-cooperative mobility service providers," European Journal of Operational Research, Elsevier, vol. 318(3), pages 802-824.
    7. Mustapha Bouhtou & Stan van Hoesel & Anton F. van der Kraaij & Jean-Luc Lutton, 2007. "Tariff Optimization in Networks," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 458-469, August.
    8. Alizadeh, S.M. & Marcotte, P. & Savard, G., 2013. "Two-stage stochastic bilevel programming over a transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 92-105.
    9. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    10. S A Gabriel & Y Shim & A J Conejo & S de la Torre & R García-Bertrand, 2010. "A Benders decomposition method for discretely-constrained mathematical programs with equilibrium constraints," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(9), pages 1404-1419, September.
    11. Wang, Zhenjie & Zhang, Dezhi & Tavasszy, Lóránt & Fazi, Stefano, 2023. "Integrated multimodal freight service network design and pricing with a competing service integrator and heterogeneous shipper classes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    12. Olivier Bochet, 2007. "Nash Implementation with Lottery Mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(1), pages 111-125, January.
    13. Joaquim Dias Garcia & Guilherme Bodin & Alexandre Street, 2024. "BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 327-335, March.
    14. Fred E. Benth & Geir Dahl & Carlo Mannino, 2012. "Computing Optimal Recovery Policies for Financial Markets," Operations Research, INFORMS, vol. 60(6), pages 1373-1388, December.
    15. Marcotte, Patrice & Savard, Gilles & Zhu, Daoli, 2009. "Mathematical structure of a bilevel strategic pricing model," European Journal of Operational Research, Elsevier, vol. 193(2), pages 552-566, March.
    16. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.
    17. van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    18. José Correa & Tobias Harks & Vincent J. C. Kreuzen & Jannik Matuschke, 2017. "Fare Evasion in Transit Networks," Operations Research, INFORMS, vol. 65(1), pages 165-183, February.
    19. S. Dempe & A. Zemkoho, 2012. "Bilevel road pricing: theoretical analysis and optimality conditions," Annals of Operations Research, Springer, vol. 196(1), pages 223-240, July.
    20. François Gilbert & Patrice Marcotte & Gilles Savard, 2014. "Mixed-logit network pricing," Computational Optimization and Applications, Springer, vol. 57(1), pages 105-127, January.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:unm:umamet:2006043. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Andrea Willems or Leonne Portz (email available below). General contact details of provider: https://edirc.repec.org/data/meteonl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.