Thesis (Ph. D.)--University of Rochester. Dept. of Economics, 2012.
"Chapters 2, 3 and 4 are based upon a paper as the result of joint work with Siwei Chen"--Foreword.
This thesis is a collection of essays on matching and resource allocation problems. In Chapters 1 and 2, we study college admission. Each college has strict preferences over sets of students, and each student has preferences over colleges. In Chapter 1, we allow monetary transfers, e.g., students may receive stipends from colleges. We specify a fixed budget for each college. The preferences of the students are over college-stipend bundles. We define pairwise stability. We construct an algorithm. The rule defined through this algorithm is not only pairwise stable but also incentive compatible for the students. In Chapter 2, we consider a central exam students should take. We allow different students to receive the same scores. We define and study an eligibility criterion. Students are divided into two groups: those who are eligible to apply to colleges, and those who are not. Eligibility respects the students’ scores. We introduce three notions of stability that respect eligibility. We define three new rules, each of which satisfies a different notion of stability. We also study an incentive compatibility requirement. Chapters 3 and 4 investigate the implications of a robustness principle for different resource allocation problems. In Chapter 3, we study the problem of assigning a set of objects, e.g., houses or tasks, to a group of individuals having preferences over these objects. We may observe cases when there are more or fewer of objects to be allocated than was planned. We formulate these changes in two new robustness properties. We characterize the family of rules that satisfy either of these properties, together with efficiency, fairness and incentive compatibility requirements. They are the sequential priority rules. In Chapter 4, we study the problem of allocating a divisible good among a group of people. Each person’s preferences are single-peaked. Here too, we may observe the cases when there might be more or fewer of resources to be allocated than was planned. We formulate changes in a robustness property. We show that there is a unique rule that is efficient and fair, and satisfies our composition property. This rule is the uniform rule.