IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v276y2019i3p947-956.html
   My bibliography  Save this article

Toll caps in privatized road networks

Author

Listed:
  • Harks, Tobias
  • Schröder, Marc
  • Vermeulen, Dries

Abstract

We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap. The first question we want to answer is how such a cap should be designed in order to minimize the total congestion. We provide an algorithm that finds an optimal price cap for networks with affine latency functions and a full support Wardrop equilibrium. Second, we consider the induced network performance at an optimal price cap. We show that for two link networks with affine latency functions, the congestion costs at the optimal price cap are at most 8/7 times the optimal congestion costs. For more general latency functions, this bound goes up to 2 under the assumption that an uncapped Nash equilibrium exists. However, in general such an equilibrium need not exist and this can be used to show that optimal price caps can induce arbitrarily inefficient flows.

Suggested Citation

  • Harks, Tobias & Schröder, Marc & Vermeulen, Dries, 2019. "Toll caps in privatized road networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 947-956.
    • Handle: RePEc:eee:ejores:v:276:y:2019:i:3:p:947-956
    DOI: 10.1016/j.ejor.2019.01.059
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719300943
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.01.059?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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.
    2. Ramesh Johari & Gabriel Y. Weintraub & Benjamin Van Roy, 2010. "Investment and Market Structure in Industries with Congestion," Operations Research, INFORMS, vol. 58(5), pages 1303-1317, October.
    3. Porter, Robert H & Zona, J Douglas, 1993. "Detection of Bid Rigging in Procurement Auctions," Journal of Political Economy, University of Chicago Press, vol. 101(3), pages 518-538, June.
    4. Roberto Cominetti & José R. Correa & Nicolás E. Stier-Moses, 2009. "The Impact of Oligopolistic Competition in Networks," Operations Research, INFORMS, vol. 57(6), pages 1421-1437, December.
    5. Carlos F. Daganzo & Yosef Sheffi, 1977. "On Stochastic Models of Traffic Assignment," Transportation Science, INFORMS, vol. 11(3), pages 253-274, August.
    6. Daron Acemoglu & Asuman Ozdaglar, 2007. "Competition and Efficiency in Congested Markets," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 1-31, February.
    7. Dial, Robert B., 2000. "Minimal-revenue congestion pricing Part II: An efficient algorithm for the general case," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 645-665, November.
    8. Dial, Robert B., 1999. "Minimal-revenue congestion pricing part I: A fast algorithm for the single-origin case," Transportation Research Part B: Methodological, Elsevier, vol. 33(3), pages 189-202, April.
    9. Cheng Wan, 2016. "Strategic decentralization in binary choice composite congestion games," Post-Print hal-02885837, HAL.
    10. Wan, Cheng, 2016. "Strategic decentralization in binary choice composite congestion games," European Journal of Operational Research, Elsevier, vol. 250(2), pages 531-542.
    11. Xiao, Feng & Yang, Hai & Han, Deren, 2007. "Competition and efficiency of private toll roads," Transportation Research Part B: Methodological, Elsevier, vol. 41(3), pages 292-308, March.
    12. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    13. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.
    14. Guo, Xiaolei & Yang, Hai & Liu, Tian-Liang, 2010. "Bounding the inefficiency of logit-based stochastic user equilibrium," European Journal of Operational Research, Elsevier, vol. 201(2), pages 463-469, March.
    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. Herty, Michael & Steffensen, Sonja & Thünen, Anna, 2022. "Multiscale control of Stackelberg games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 468-488.
    2. Michael Herty & Sonja Steffensen & Anna Thunen, 2020. "Multiscale Control of Stackelberg Games," Papers 2011.03405, arXiv.org.
    3. Chen, Zhiyuan & Sun, Shaobo & Li, Jianbin & Zhang, Langlang & Fan, Hao, 2022. "Optimal BOT contracts in a two-road transportation network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    4. Wang, Aihu & Tang, Yuanhua & Mohmand, Yasir Tariq & Xu, Pei, 2022. "Modifying link capacity to avoid Braess Paradox considering elastic demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    5. Pieter Kleer, 2023. "Price of anarchy for parallel link networks with generalized mean objective," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 27-55, March.
    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. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Monotonicity of equilibria in nonatomic congestion games," European Journal of Operational Research, Elsevier, vol. 316(2), pages 754-766.

    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. Liu, Tian-Liang & Chen, Jian & Huang, Hai-Jun, 2011. "Existence and efficiency of oligopoly equilibrium under toll and capacity competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 908-919.
    2. 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.
    3. Patrick Maillé & Nicolás E. Stier-Moses, 2009. "Eliciting Coordination with Rebates," Transportation Science, INFORMS, vol. 43(4), pages 473-492, November.
    4. Tobias Harks & Konstantin Miller, 2011. "The Worst-Case Efficiency of Cost Sharing Methods in Resource Allocation Games," Operations Research, INFORMS, vol. 59(6), pages 1491-1503, December.
    5. Melo, Emerson, 2014. "Price competition, free entry, and welfare in congested markets," Games and Economic Behavior, Elsevier, vol. 83(C), pages 53-72.
    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. Roberto Cominetti & José R. Correa & Nicolás E. Stier-Moses, 2009. "The Impact of Oligopolistic Competition in Networks," Operations Research, INFORMS, vol. 57(6), pages 1421-1437, December.
    8. Chinmay Maheshwari & Kshitij Kulkarni & Druv Pai & Jiarui Yang & Manxi Wu & Shankar Sastry, 2024. "Congestion Pricing for Efficiency and Equity: Theory and Applications to the San Francisco Bay Area," Papers 2401.16844, arXiv.org, revised Sep 2024.
    9. Yang, Hai & Wang, Xiaolei, 2011. "Managing network mobility with tradable credits," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 580-594, March.
    10. Qi, Jin & Sim, Melvyn & Sun, Defeng & Yuan, Xiaoming, 2016. "Preferences for travel time under risk and ambiguity: Implications in path selection and network equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 264-284.
    11. Haoning Xi & Liu He & Yi Zhang & Zhen Wang, 2020. "Bounding the efficiency gain of differentiable road pricing for EVs and GVs to manage congestion and emissions," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-36, July.
    12. Han, Deren & Lo, Hong K. & Sun, Jie & Yang, Hai, 2008. "The toll effect on price of anarchy when costs are nonlinear and asymmetric," European Journal of Operational Research, Elsevier, vol. 186(1), pages 300-316, April.
    13. Rambha, Tarun & Boyles, Stephen D. & Unnikrishnan, Avinash & Stone, Peter, 2018. "Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 104-121.
    14. Georgia Perakis & Wei Sun, 2014. "Efficiency Analysis of Cournot Competition in Service Industries with Congestion," Management Science, INFORMS, vol. 60(11), pages 2684-2700, November.
    15. Anny B. Wang & W. Y. Szeto, 2020. "Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery," Networks and Spatial Economics, Springer, vol. 20(2), pages 395-422, June.
    16. Randall Berry & Michael Honig & Thành Nguyen & Vijay Subramanian & Rakesh Vohra, 2020. "The Value of Sharing Intermittent Spectrum," Management Science, INFORMS, vol. 66(11), pages 5242-5264, November.
    17. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.
    18. E. Nikolova & N. E. Stier-Moses, 2014. "A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel Times," Operations Research, INFORMS, vol. 62(2), pages 366-382, April.
    19. Raimondo, Roberto, 2020. "Pathwise smooth splittable congestion games and inefficiency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 15-23.
    20. Ehrgott, Matthias & Wang, Judith Y.T. & Watling, David P., 2015. "On multi-objective stochastic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 704-717.

    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:eee:ejores:v:276:y:2019:i:3:p:947-956. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.