# Seattle 2022

## Lecture series

# Gross substitutes, optimal transport and matching models

*Optimal Transport Summer School, the University of Washington, Seattle, June 19-July 1, 2022*

### Content

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.

### Schedule

TBD

### Course material

The lecture slides are available before each lecture from the following github repository.

### References

These lectures will be loosely based on my math+econ+code lectures:

A. Galichon, ‘math+econ+code’ masterclass on equilibrium transport and matching models in economics. June 2021. Available here.

### Outline

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.