Gross substitutes, optimal transport and matching models: Lecture 2

Speaker: Alfred Galichon

Date: Tue, Jun 28, 2022

Location: PIMS, University of Washington, Zoom, Online

Conference: PIMS- IFDS- NSF Summer School on Optimal Transport

Subject: Mathematics

Class: Scientific


Gross substitutes is a fundamental property in mathematics, economics and computation, almost as important as convexity. It is at the heart of optimal transport theory – although this is often underrecognized – and understanding the connection key to understanding the extension of optimal transport to other models of matching.

Lecture 1. Introduction to gross substitutes M-matrices and M-maps, nonlinear Perron-Froebenius theory, convergence of Jacobi algorithm. A toy hedonic model.

Lecture 2. Models of matching with transfers Problem formulation, regularized and unregularized case. IPFP and its convergence. Existence and uniqueness of an equilibrium. Lattice structure.

Lecture 3. Models of matching without transfers Gale and Shapley’s stable matchings. Adachi’s formulation. Kelso-Craford. Hatfield-Milgrom.