A solution to matching with preferences over colleagues

We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents' preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty

A Solution to Matching with Preferences over Colleagues

We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents’ preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty

Matching with Externalities

We incorporate externalities into the stable matching theory of two-sided markets. Extending theclassical substitutes condition to markets with externalities, we establish that stable matchings exist whenagent choices satisfy substitutability. We show that substitutability is a necessary condition for the existenceof a stable matching in a maximal-domain sense and provide a characterization of substitutable choicefunctions. In addition, we extend the standard insights of matching theory, like the existence of side-optimal stable matchings and the deferred acceptance algorithm, to settings with externalities even thoughthe standard fixed-point techniques do not appl

How to Control Controlled School Choice

We characterize choice rules for schools that regard students as substitutes while expressing preferences for a diverse student body. The stable (or fair) assignment of students to schools requires the latter to regard the former as substitutes. Such a requirement is in conflict with the reality of schools' preferences for diversity. We show that the conflict can be useful, in the sense that certain unique rules emerge from imposing both considerations. We also provide welfare comparisons for students when different choice rules are employed

Median Stable Matching

We define the median stable matching for two-sided matching markets with side payments and prove constructively that it exists.

A Solution to Matching with Preferences over Colleagues

We study many-to-one matchings, such as the assignment of students to colleges, where the students have preferences over the other students who would attend the same college. It is well known that the core of this model may be empty, without strong assumptions on agents’ preferences. We introduce a method that finds all core matchings, if any exist. The method requires no assumptions on preferences. Our method also finds certain partial solutions that may be useful when the core is empty

Efficient Market Design with Distributional Objectives

Given an initial matching and a policy objective on the distribution of agent types to institutions, we study the existence of a mechanism that weakly improves the distributional objective and satisfies constrained efficiency, individual rationality, and strategy-proofness. We show that such a mechanism need not exist in general. We introduce a new notion of discrete concavity, which we call pseudo M$^{\natural}$-concavity, and construct a mechanism with the desirable properties when the distributional objective satisfies this notion. We provide several practically relevant distributional objectives that are pseudo M$^{\natural}$-concave