IDEAS home Printed from https://ideas.repec.org/p/hal/spmain/hal-02173210.html

Optimal transport on large networks a practitioner guide

Author

Listed:
  • Arthur Charpentier

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, DMS - Département de Mathématiques et de statistique [UdeM- Montréal] - UQAM - Université du Québec à Montréal = University of Québec in Montréal)

  • Alfred Galichon

    (CIMS - Courant Institute of Mathematical Sciences [New York] - NYU - New York University [New York] - NYU - NYU System)

  • Lucas Vernet

    (Sciences Po - Sciences Po, Banque de France - Banque de France - Banque de France)

Abstract

This article presents a set of tools for the modeling of a spatial allocation problem in a large geographic market and gives examples of applications. In our settings, the market is described by a network that maps the cost of travel between each pair of adjacent locations. Two types of agents are located at the nodes of this network. The buyers choose the most competitive sellers depending on their prices and the cost to reach them. Their utility is assumed additive in both these quantities. Each seller, taking as given other sellers prices, sets her own price to have a demand equal to the one we observed. We give a linear programming formulation for the equilibrium conditions. After formally introducing our model we apply it on two examples: prices offered by petrol stations and quality of services provided by maternity wards. These examples illustrate the applicability of our model to aggregate demand, rank prices and estimate cost structure over the network. We insist on the possibility of applications to large scale data sets using modern linear programming solvers such as Gurobi. In addition to this paper we released a R toolbox to implement our results and an online tutorial (http://optimalnetwork.github.io) .

Suggested Citation

  • Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks a practitioner guide," Sciences Po Economics Publications (main) hal-02173210, HAL.
    • Handle: RePEc:hal:spmain:hal-02173210
    Note: View the original document on HAL open archive server: https://hal.science/hal-02173210v1
    as

    Download full text from publisher

    File URL: https://hal.science/hal-02173210v1/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Treb Allen & Costas Arkolakis, 2014. "Trade and the Topography of the Spatial Economy," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1085-1140.
    2. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    3. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    4. Alfred Galichon, 2016. "Optimal transport methods in economics," Sciences Po Economics Publications (main) hal-03256830, HAL.
    5. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870, December.
    6. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    7. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    8. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    9. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    10. Eckert, Andrew & West, Douglas S, 2004. "Retail Gasoline Price Cycles across Spatially Dispersed Gasoline Stations," Journal of Law and Economics, University of Chicago Press, vol. 47(1), pages 245-273, April.
    11. Severin Borenstein & A. Colin Cameron & Richard Gilbert, 1997. "Do Gasoline Prices Respond Asymmetrically to Crude Oil Price Changes?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(1), pages 305-339.
    12. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
    Full references (including those not matched with items on IDEAS)

    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. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks, a practitioner's guide," Papers 1907.02320, arXiv.org, revised Aug 2019.
    2. Arthur Charpentier & Alfred Galichon & Lucas Vernet, 2019. "Optimal transport on large networks a practitioner guide," Working Papers hal-02173210, HAL.
    3. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    4. Susanne Schennach & Vincent Starck, 2025. "Optimally-Transported Generalized Method of Moments," Papers 2511.05712, arXiv.org.
    5. Itai Arieli & Yakov Babichenko & Fedor Sandomirskiy, 2023. "Feasible Conditional Belief Distributions," Papers 2307.07672, arXiv.org, revised Nov 2024.
    6. Andrew Lyasoff, 2023. "The Time-Interlaced Self-Consistent Master System of Heterogeneous-Agent Models," Papers 2303.12567, arXiv.org, revised May 2025.
    7. Andrei Voronin, 2025. "Generalized Optimal Transport," Papers 2507.22422, arXiv.org.
    8. Roger Koenker, 2017. "Quantile regression 40 years on," CeMMAP working papers 36/17, Institute for Fiscal Studies.
    9. Kuan‐Ming Chen & Yu‐Wei Hsieh & Ming‐Jen Lin, 2023. "Reducing Recommendation Inequality Via Two‐Sided Matching: A Field Experiment Of Online Dating," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1201-1221, August.
    10. Keita Sunada & Kohei Izumi, 2025. "Optimal treatment assignment rules under capacity constraints," Papers 2506.12225, arXiv.org, revised Sep 2025.
    11. Yagan Hazard & Toru Kitagawa, 2025. "Who With Whom? Learning Optimal Matching Policies," Papers 2507.13567, arXiv.org.
    12. Alderighi, Marco & Baudino, Marco, 2015. "The pricing behavior of Italian gas stations: Some evidence from the Cuneo retail fuel market," Energy Economics, Elsevier, vol. 50(C), pages 33-46.
    13. Alfred Galichon & Bernard Salanié, 2023. "Structural Estimation of Matching Markets with Transferable Utility," Post-Print hal-03935865, HAL.
    14. Ashwin Kambhampati & Carlos Segura‐Rodriguez, 2022. "The optimal assortativity of teams inside the firm," RAND Journal of Economics, RAND Corporation, vol. 53(3), pages 484-515, September.
    15. Adam Bouyamourn, 2025. "Where to Experiment? Site Selection Under Distribution Shift via Optimal Transport and Wasserstein DRO," Papers 2511.04658, arXiv.org.
    16. Wayne Yuan Gao & Rui Wang, 2023. "IV Regressions without Exclusion Restrictions," Papers 2304.00626, arXiv.org, revised Jul 2023.
    17. Haiyan Liu & Bin Wang & Ruodu Wang & Sheng Chao Zhuang, 2023. "Distorted optimal transport," Papers 2308.11238, arXiv.org, revised May 2025.
    18. Principi, Giulio & Wakker, Peter P. & Wang, Ruodu, 2025. "Anticomonotonicity for preference axioms: The natural counterpart to comonotonicity," Theoretical Economics, Econometric Society, vol. 20(3), July.
    19. Arthur Charpentier & Emmanuel Flachaire & Ewen Gallic, 2023. "Optimal Transport for Counterfactual Estimation: A Method for Causal Inference," Papers 2301.07755, arXiv.org.
    20. Beatrice Acciaio & Berenice Anne Neumann, 2025. "Characterization of transport optimizers via graphs and applications to Stackelberg–Cournot–Nash equilibria," Mathematics and Financial Economics, Springer, volume 19, number 3, June.

    More about this item

    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:hal:spmain:hal-02173210. 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: Contact - Sciences Po Department of Economics (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.