Essays on Allocation Problems

Scarce resources are oftentimes allocated in a centralized clearinghouse based on individuals' reported preferences and objects' priorities. Prominent examples include public school assignment, allocation of dormitories, office spaces, allocation of organs to patients waiting for organ transplantation, and most recently, administration of COVID-19 vaccines. This dissertation develops and studies equitable and efficient allocation mechanisms without monetary transfers.

Chapter 2, which is a joint work with Atila Abdulkadiroglu, addresses the trade-off between efficiency and respecting priorities. We show that finding an efficient allocation that minimizes priority violations is an NP-hard problem when objects have weak priority rankings. Consequently, we focus on finding priority violations minimal mechanisms in subsets of efficient mechanisms, namely, sequential dictatorships and hierarchical exchange rules. Both classes are widely studied in the literature and applied in real-life resource allocation problems. We provide polynomial-time mechanisms that minimize priority violations in each of these classes. %Additionally, we study the possibility of minimizing priority violations in the entire class of efficient and strategyproof mechansims. We show that none of the well-known efficient and strategyproof mechanisms, such as hierarchical exchange rules or trading cycles mechanisms minimize priority violations in that class.

Chapter 3, which is also a joint work with Atila Abdulkadiroglu, studies diversity and distributional objectives in allocation problems. First, we study a single school's problem of choosing a set of applicants to be assigned to the school. We provide an axiomatic characterization of a general class of choice rules where distributional objectives are met through type-specific reserves and quotas. We show that a particular intuitive implementation of a reserves- and quotas-based rule, which we call the regular reserves-and-quotas rule, uniquely minimizes priority violations in this class. Next, we study a general setup with multiple schools. We show that when all schools use the regular reserves-and-quotas rule, the Deferred Acceptance mechanism minimizes priority violations in a large class of mechanisms that satisfy the distributional constraints.

Chapter 4 evaluates the welfare and distributional outcomes of the Deferred Acceptance mechanism in a unified framework with school choice and a housing market. In my model, families' strategically choose where to live before going through a school admission process. I show that when families receive higher priorities at neighborhood schools, the Deferred Acceptance mechanism improves aggregate or average welfare compared to neighborhood assignment. Additionally, under general conditions, the Deferred Acceptance mechanism improves the welfare of lowest-income families, both with and without neighborhood priorities. To the best of my knowledge, my work provides the first theoretical justification for using the Deferred Acceptance mechanism on the grounds of welfare and equity in a general matching model with residential choices.