UC Berkeley

Since the 2000s, matching theory has seen an increasing number of applications, from school assignments to organ donation. This dissertation collects three papers contributing to the theory of one-sided matching with endowments.

In the first chapter, I study the testable implications of the core in an exchange economy with unit demand when agents' preferences are unobserved. To do so, I develop a model of aggregate matchings in which the core is testable; the identifying assumption is that agents' preferences are solely determined by observable characteristics. I give conditions that characterize when observed economies are compatible with the core. These conditions are meaningful, intuitive, and tractable; they provide a nonparametric test for the core in the style of revealed preferences. I also develop a parametric method to estimate preference parameters from multiple observations of exchange economies. An allocation being in the core implies necessary moment inequalities, which I leverage to obtain partial identification.

The second chapter is coauthored with Will Sandholtz. We study the classic house-swapping problem of Shapley and Scarf (1974) in a setting where agents may have “objective” indifferences, i.e., indifferences that are shared by all agents. In other words, if any one agent is indifferent between two houses, then all agents are indifferent between those two houses. The most direct interpretation is the presence of multiple copies of the same object. Our setting is a special case of the house-swapping problem with general indifferences. We derive a simple, easily interpretable algorithm that produces the unique strict core allocation of the house-swapping market, if it exists. Our algorithm runs in O(n^{2}) time, where n is the number of agents and houses. This is an improvement over the O(n^{3}) time methods for the more general problem.

The third chapter is also coauthored with Will Sandholtz. We note that the proof of Bird (1984), the first to show group strategy-proofness of top trading cycles (TTC), requires a correction. We provide a counter-example to a critical claim, then present a corrected proof in the spirit of the original.