The Strong Core of Housing Markets with Partial Order Preferences

TL;DR

This paper analyzes the strong core in housing markets where agents have partial order preferences, providing structural insights, an efficient algorithm, and extending known results to this setting.

Contribution

It offers a structural characterization and an efficient algorithm for the strong core with partial order preferences, extending previous results from weak orders.

Findings

Algorithm finds a strong core allocation or determines emptiness

Strong core respects improvements in preferences

Algorithm is group-strategyproof

Abstract

We study the strong core of housing markets when agents' preferences over houses are expressed as partial orders. We provide a structural characterization of the strong core, and propose an efficient algorithm that finds an allocation in the strong core or decides that it is empty, even in the presence of forced and forbidden arcs. The algorithm satisfies the property of group-strategyproofness. Additionally, we show that certain results known for the strong core in the case when agents' preferences are weak orders can be extended to the setting with partial order preferences; among others, we show that the strong core in such housing markets satisfies the property of respecting improvements.