Selected open problems in Matching Under Preferences

Abstract

The House Allocation problem, the Stable Marriage problem and the Stable Roommates problem are three fundamental problems in the area of matching under preferences. These problems have been studied for decades under a range of optimality criteria, but despite much progress, some chal- lenging questions remain open. The purpose of this article is to present a range of key open questions for each of these problems, which will hope- fully stimulate further research activity in this area.