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Optimal transport on large networks a practitioner guide

Author

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  • 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," SciencePo Working papers Main hal-02173210, HAL.
    • Handle: RePEc:hal:spmain:hal-02173210
    Note: View the original document on HAL open archive server: https://hal.science/hal-02173210
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    References listed on IDEAS

    as
    1. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    2. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    3. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    4. Pablo D. Fajgelbaum & Edouard Schaal, 2020. "Optimal Transport Networks in Spatial Equilibrium," Econometrica, Econometric Society, vol. 88(4), pages 1411-1452, July.
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    7. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
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    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.
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