Dynamic Reserves in Matching Markets

We study a school choice problem under affirmative action policies where authorities reserve a certain fraction of the slots at each school for specific student groups, and where students have preferences not only over the schools they are matched to but also the type of slots they receive. Such reservation policies might cause waste in instances of low demand from some student groups. To propose a solution to this issue, we construct a family of choice functions, dynamic reserves choice functions, for schools that respect within-group fairness and allow the transfer of otherwise vacant slots from low-demand groups to high-demand groups. We propose the cumulative offer mechanism (COM) as an allocation rule where each school uses a dynamic reserves choice function and show that it is stable with respect to schools' choice functions, is strategy-proof, and respects improvements. Furthermore, we show that transferring more of the otherwise vacant slots leads to strategy-proof Pareto improvement under the COM

Essays in Market Design

Thesis advisor: Utku UnverThis dissertation consists of two chapters. The first chapter: Dynamic reserves in matching markets with contracts. In this paper we study a matching problem where agents care not only about the institution they are assigned to but also about the contractual terms of their assignment so that they have preferences over institution-contractual term pairs. Each institution has a target distribution of its slots reserved for different contractual terms. If there is less demand for some groups of slots, then the institution is given opportunity to redistribute unassigned slots over other groups. The choice function we construct takes the capacity of each group of seats to be a function of number of vacant seats of groups considered earlier. We advocate the use of a cumulative offer mechanism (COM) with overall choice functions designed for institutions that allow capacity transfer across different groups of seats as an allocation rule. In applications such as engineering school admissions in India, cadet-branch matching problems at the USMA and ROTC where students are ranked according to test scores (and for each group of seats, corresponding choice functions are induced by them), we show that the COM with a monotonic capacity transfer scheme produces stable outcomes, is strategy proof, and respect improvements in test scores. Allowing capacity redistribution increases efficiency. The outcome of the COM with monotone capacity transfer scheme Pareto dominates the outcome of the COM with no capacity transfer. The second chapter: On relationships between substitutes conditions. In the matching with contracts literature, three well-known conditions on choice functions (from stronger to weaker)- substitutability, unilateral substitutability (US) and bilateral substitutability (BS) have proven to be critical. This paper aims to deepen our understanding of them by separately axiomatizing the gap between the BS and the other two. We first introduce a new “doctor separability” (DS) condition and show that BS, DS and irrelevance of rejected contracts (IRC) are equivalent to IRC and US. Due to Hatfield and Kojima (2010) and Aygün and Sönmez (2012), it is known that US, “Pareto separability” (PS), and IRC are equivalent to substitutability and IRC. This, along with our result, implies that BS, DS, PS, and IRC are equivalent to substitutability and IRC. All of these results are given without IRC whenever hospital choices are induced from preferences.Thesis (PhD) — Boston College, 2015.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Economics

An analysis of dynamic bankruptcy problems

In this paper, we analyse Pareto optimal and strategy-proof allocation rules on the dynamic bankruptcy domain. We first develop a model in which dynamic bankruptcy problems are defined. We then redefine the well-known axioms of the classical bankruptcy literature for the dynamic case. In our analysis, for simplicity, two agents and two periods are considered. We first characterize Pareto optimal allocations on the dynamic bankruptcy domain. The main result of the paper characterizes the Pareto optimal and strategy-proof allocation rules on the same domain

Assignment maximization

We evaluate the goal of maximizing the number of individually rational assignments. We show that it implies incentive, fairness, and implementation impossibilities. Despite that, we present two classes of mechanisms that maximize assignments. The first are Pareto efficient, and undominated – in terms of number of assignments – in equilibrium. The second are fair for unassigned students and assign weakly more students than stable mechanisms in equilibrium. We provide comparisons with well-known mechanisms through computer simulations. Those show that the difference in number of matched agents between the proposed mechanisms and others in the literature is large and significant