Essays in Market Design

Abstract

This 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.