Econometrics, Quantitative Economics, Data Science

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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.

kindey-transplant-hackaton

Kidney transplant hackaton

a math+econ+code event

When? TBA

Who? participation to this math+econ+code event is open to the public upon request.

What? Kidney transplant problems provide a very interesting real-life examples of dynamic matching problems. A large academic literature exists on the topic, both in economics and in operations research. Because the problem is a difficult problem computationally speaking, a number of algorithms exist out there to try to approximate the best solution. This hackaton will put you in the shoes of the transplant agency: at each period, you will receive the state of your population, which is made of your existing population of patients, plus new patients and minus deceased ones (simulated by our platform). Your role will be write the algorithm that matches donors and receivers, given the constraints on the way transplants can be done (state of the patient, compatibility between donor and receiver, length of transplant chains, etc.)

Each player plays in parallel and is evaluated by a score, which will reflect the state of their population of patients. The game is played over a very large number of periods. The player with the highest final score has come up with the best algorithm and wins the hackaton.

What is required? In order to participate, you need to be familiar with Python programming. Your only input is the matching function that assigns donors to receivers — a function whose length can be less than a hundred lines but can be more depending on your design. All the interfacing is done by the platform.

Interested? contact us at math.econ.code@gmail.com.