Research

This paper studies the testable implications of the core in an exchange economy when agents' preferences are unknown. Through a revealed preferences perspective, I build a model in which the core is testable. The setting a pure exchange economy with indivisible goods and unit demand. The key identifying assumption is that agents' preferences are solely determined by observable characteristics. The setting and assumption allow me to build on earlier results and obtain if and only if conditions for rationalizability of the observed allocation. These conditions are meaningful, intuitive, and tractable. Further, the results formally link together the core, competitive equilibrium, and Afriat's theorem. I also develop a method to estimate utility parameters from repeated observations of exchange economies; the setting is akin to Fox (2010). The allocation being in the core implies necessary moment inequalities, which I use to obtain partial identification.

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 square-polynomial time, an improvement over the cubed time methods for the more general problem.

Serial dictatorship (SD) is often used to allocate indivisible objects to participants. However, when participants may be indifferent between objects, the usual implementation is not Pareto efficient. We note the correct implementation of SD, which acts on social outcomes (allocations). We also note two other descriptions of the same mechanism, which do not require participants to choose between social outcomes.