Essays in Matching Theory and Mechanism Design

Abstract

This dissertation consists of three chapters. The first chapter consists of a survey of the literature on affirmative action and diversity objective in school choice mechanisms. It presents and analyzes some of the main papers on the subject, showing the evolution of our understanding of the effects that different affirmative action policies have on the welfare and fairness of student assignments, the satisfaction of the diversity objectives as well as the domain of policies that allows for stable outcomes. The second chapter analyzes the problem of school choice mechanisms when policy-makers have objectives over the distribution of students by type across the schools. I show that mechanisms currently available in the literature may fail to a great extent in satisfying those objectives, and introduce a new one, which satisfies two properties. First, it produces assignments that satisfy a fairness criterion which incorporates the diversity objectives as an element of fairness. Second, it approximates optimally the diversity objectives while still satisfying the fairness criterion. We do so by embedding "preference" for those objectives into the schools' choice functions in a way that satisfies the substitutability condition and then using the school-proposing deferred acceptance procedure. This leads to the equivalence of stability with the desired definition of fairness and the maximization of those diversity objectives among the set of fair assignments. A comparative analysis also shows analytically that the mechanism that we provide has a general ability to satisfy those objectives, while in many familiar classes of scenarios the alternative ones yield segregated assignments. Finally, we analyze the incentives induced by the proposed mechanism in different market sizes and informational structures. The third chapter (co-authored with Orhan Aygün) presents an analysis of the Brazilian affirmative action initiative for access to public federal universities. In August 2012 the Brazilian federal government enacted a law mandating the prioritization of students who claim belonging to the groups of those coming from public high schools, low income families and being racial minorities to defined proportions of the seats available in federal public universities. In this problem, individuals may be part of one or more of those groups, and it is possible for students not to claim some of the privileges associated with them. This turns out to be a problem not previously studied in the literature. We show that under the choice function induced by the current guidelines, students may be better off by not claiming privileges that they are eligible to. Moreover, the resulting assignments may not be fair or satisfy the affirmative action objectives, even when there are enough students claiming low--income and minority privileges. Also, any stable mechanism that uses the current choice functions is neither incentive compatible nor fair. We propose a new choice function to be used by the universities that guarantees that a student will not be worse off by claiming an additional privilege, is fair and satisfies the affirmative action objectives whenever it is possible and there are enough applications claiming low--income and minority privileges. Next, we suggest a stable, incentive compatible and fair mechanism to create assignments for the entire system.