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A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing

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Author Info

  • Martine Labbé

    (Institut de Statistique et Recherche Opérationnelle, Université Libre de Bruxelles, Boulevard du Triomphe, CP 210/01, B-1050 Bruxelles, Belgique)

  • Patrice Marcotte

    (Centre de recherche sur les Transports and Département d'Informatique et Recherche Opérationnelle, Université de Montréal, CP 6128, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3J7)

  • Gilles Savard

    (GERAD and Département de mathématiques et génie industriel, Ecole Polytechnique de Montréal, CP 6079, Succursale Centre-Ville, Montréal, Québec, Canada H3C 3A7)

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    Abstract

    We consider a bilevel model where the leader wants to maximize revenues from a taxation scheme, while the follower rationally reacts to those tax levels. We focus our attention on the special case of a toll-setting problem defined on a multicommodity transportation network. We show that the general problem is NP-complete, while particular instances are polynomially solvable. Numerical examples are given.

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    File URL: http://dx.doi.org/10.1287/mnsc.44.12.1608
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 44 (1998)
    Issue (Month): 12-Part-1 (December)
    Pages: 1608-1622

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    Handle: RePEc:inm:ormnsc:v:44:y:1998:i:12-part-1:p:1608-1622

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    Related research

    Keywords: Pricing; Networks; Bilevel;

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    Citations

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    Cited by:
    1. 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.
    2. Van Dender, Kurt, 2004. "Pricing transport networks with fixed residential location," Regional Science and Urban Economics, Elsevier, vol. 34(3), pages 289-307, May.
    3. Jean Etoa, 2010. "Solving convex quadratic bilevel programming problems using an enumeration sequential quadratic programming algorithm," Journal of Global Optimization, Springer, vol. 47(4), pages 615-637, August.
    4. Losada, Chaya & Scaparra, M. Paola & O’Hanley, Jesse R., 2012. "Optimizing system resilience: A facility protection model with recovery time," European Journal of Operational Research, Elsevier, vol. 217(3), pages 519-530.
    5. Hoesel, Stan van, 2006. "An overview of Stackelberg pricing in networks," Research Memorandum 043, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. François Gilbert & Patrice Marcotte & Gilles Savard, 2014. "Mixed-logit network pricing," Computational Optimization and Applications, Springer, vol. 57(1), pages 105-127, January.
    7. Hoesel,Stan,van & Kraaij,Anton F.,van der & Mannino,Carlo & Bouhtou,Mustapha & Oriolo,Gianpaolo, 2003. "Polynomial cases of the tarification problem," Research Memorandum 063, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    8. Steven Gabriel & Sauleh Siddiqui & Antonio Conejo & Carlos Ruiz, 2013. "Solving Discretely-Constrained Nash–Cournot Games with an Application to Power Markets," Networks and Spatial Economics, Springer, vol. 13(3), pages 307-326, September.
    9. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2004. "Modeling private highways in networks with entry-exit based toll charges," Transportation Research Part B: Methodological, Elsevier, vol. 38(3), pages 191-213, March.
    10. Dung-Ying Lin & Avinash Unnikrishnan & S. Waller, 2011. "A Dual Variable Approximation Based Heuristic for Dynamic Congestion Pricing," Networks and Spatial Economics, Springer, vol. 11(2), pages 271-293, June.
    11. Hoesel,Stan,van, 2005. "An overview of Stackelberg pricing in networks," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    12. Grigoriev,Alexander & Hoesel,Stan,van & Kraaij,Anton F.,van der & Marc,Uetz & Mustapha,Bouhtou, 2004. "Pricing Network Edges to Cross a River," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    13. 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.
    14. 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.
    15. Budnitzki, Alina, 2014. "Computation of the optimal tolls on the traffic network," European Journal of Operational Research, Elsevier, vol. 235(1), pages 247-251.
    16. Fred E. Benth & Geir Dahl & Carlo Mannino, 2010. "Computing optimal recovery policies for financial markets," DIS Technical Reports 2010-20, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    17. Chen, Mei & Bernstein, David H., 2004. "Solving the toll design problem with multiple user groups," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 61-79, January.

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