### PhD Defense

It is my pleasure to invite you to the defense of my PhD thesis on **Wednesday, December 15th 2021, at 14:00**.

- The defense will take place in Amphithéatre Gouges 1 (see map below).
- If you prefer to attend online, a livestream will be available on YouTube.
- My manuscript is available here.

#### Analysis of Random Models for Stable Matchings

In a two sided matching market, two types of agents have preferences over one another. Examples include college admissions (students and colleges), residency programs (doctors and hospitals), job markets (workers and jobs) and, in the classical analogy, stable marriages (men and women). In a founding paper, Gale and Shapley introduced the deferred acceptance procedure, where one side proposes and the other disposes, which computes a stable matching.

Stable matchings have been an extensive research topic in computer science and economics. Results in the computer science literature include the lattice structure of the set of stable matchings, and algorithms to compute it. In the economics literature, researcher have studied the incentives of agents taking part in two-sided matching markets, both from the theoretical and empirical point of views.

A recent line of works study the properties of stable matchings, using stochastic models of two-sided matching markets where the preferences of agents are drawn at random. This thesis follows this direction of inquiry, and considers two main questions: “who can manipulate?” and “who gets what?”.

The first part, addressing the question “who can manipulate?”, contains three different results. In a first result (Chapter 4), we show that when one side of the market has strongly correlated preferences, incentives to manipulate are reduced. In a second result (Chapter 5), we show that uncorrelated preferences is a worst case situation when compared to correlated preferences. Proofs of both results are based on a randomized analysis of the algorithm which computes the incentives agents have to manipulate. In a third result (Chapter 6), we study the incomplete information game where students must apply to a limited number of schools, and thus report their preferences strategically. We prove the existence of symmetric equilibria and design algorithms to compute equilibria in various special cases.

The second part, addressing the question “who gets what?”, also contains three different results. In a first result (Chapter 7), we show that under a certain input distribution of preferences, the two variants of deferred acceptance produce the same output distribution on matchings. Proofs use the lattice structure of stable matchings, show that a fixed matching has the same probability of being the top or bottom element, and give a closed formula for the probability of two agents being matched. In a second result (Chapter 8), we consider a model where the probabilities that agents like each are quantified by a “popularity” matrix, and we give evidences that the probabilities that deferred acceptance matches agents is asymptotically given by the scaled matrix where lines/columns sum up to 1. In a third result (Chapter 9), we study the time complexity of deferred acceptance, which relates to the rank people from the proposing side give to their partner. Proofs are based on a reduction to the coupon collector's problem.