Inference on the equilibrium flow problem

Research retreat and mini-workshop held at the IASC Cargese, Corsica, France, April 21-26, 2025

Organizers: Alfred Galichon (New York University and Sciences Po) and Antoine Jacquet (Sciences Po)

Funded by the European Research Council grant ERC-CoG No. 866274 “EQUIPRICE”.

This event combines a research retreat and a mini-workshop both seeking to cross perspectives in the construction of a general framework for estimation of the “equilibrium flow problem”. The “equilibrium flow problem,” extends minimum cost flow problems in order to provide a unified network-based framework to analyze problems such as matching problems, multinomial choice problems, hedonic pricing problems, shortest path problems, dynamic programming problems, international trade flows. The equilibrium flow problem is a far-reaching extension of Optimal Transport, and thus, this project can be seen as an extension of the increasingly popular topic of “Inverse Optimal Transport”.
We have been studying the mathematical properties of the problem, with questions such as existence of equilibrium prices, investigating possible uniqueness, and lattice structure, and special attention paid to the Nontransferable Utility (NTU) limit of the problem, which, in the bipartite case, provides the Gale and Shapley stable marriage problem. An inferential theory is build using maximum likelihood estimation and minimax-regret estimators. Model selection is incorporated to estimation procedures; more precisely, the proximal mapping operator will be inserted in between two iterative phases of these procedures. Several applications are developed, one to the gravity equation in international trade, one to hedonic models, one to matching models.

Investigators and speakers:

• Guillaume Carlier (Dauphine)
• Alfred Galichon (NYU and Sciences Po)
• Pierre Jacob (ESSEC)
• Antoine Jacquet (Sciences Po)
• Jean-Bernard Lasserre (Toulouse School of Economics)
• Guillaume Pouliot (University of Chicago)
• Maxime Sylvestre (Dauphine)

Talks are accessible to the public (on zoom) but registration is mandatory by emailing antoine.jacquet@sciencespo.fr.

Monday April 21, 2025

Morning: arrival and welcome coffee

Afternoon:
230pm – 330pm: Opening session, “leveling the playing field: what are the main results we are after?” (led by Antoine Jacquet and Maxime Sylvestre)
330pm – 4pm: coffee break.
4pm – 6pm: group work session.

Tuesday April 22, 2025

Morning
930am – 1030am: Guillaume Carlier, TBA.
1030am – 11am: coffee break.
11am – 1230pm: group work session.

Afternoon
230pm – 330pm: Maxime Sylvestre, “Convergence of a hybrid scheme for the computation of weak inverse optimal transport”.
330pm – 4pm: coffee break.
4pm – 6pm: group work session.

Wednesday April 23, 2025

Morning
930am – 1030am: Jean-Bernard Lasserr.e, “Gaussian mixtures closest to a given measure via optimal transport”.
1030am – 11am: coffee break.
11am – 1230pm: group work session.

Afternoon: free time

Thursday April 24, 2025

Morning
930am – 1030am: Antoine Jacquet, “Computation of NTU aggregate equilibria with a finite-time Newton-Jacobi method.”
1030am – 11am: coffee break.
11am – 1230pm: group work session.

Afternoon
230pm – 330pm: Pierre Jacob, “Optimal transport and related problems in the field of Monte Carlo methods.”
330pm – 4pm: coffee break.
4pm – 6pm: group work session.

Friday April 25, 2025

Morning
1030am – 1030am: Alfred Galichon, “Some partial results on the inference in ITU matching models using LCP theory.”
1030am – 11am: coffee break.
11am – 1230pm: group work session.

Afternoon
230pm -330pm: Guillaume Pouliot, TBA.
330pm – 4pm: coffee break.
4pm – 6pm: group work session.

Saturday April 26, 2025

Morning
Departure