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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
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    References listed on IDEAS

    as
    1. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870, December.
    2. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
    3. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    4. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    5. 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.
    6. Heijnen, Pim & Soetevent, Adriaan R., 2018. "Price competition on graphs," Journal of Economic Behavior & Organization, Elsevier, vol. 146(C), pages 161-179.
    7. 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.
    8. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    9. 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.
    10. Alfred Galichon, 2016. "Optimal transport methods in economics," Sciences Po Economics Publications (main) hal-03256830, HAL.
    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.
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