Rank Gaps and the Size of the Core for Roommate Problems


This paper deals with roommate problems (Gale and Shapley, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study the assortativeness of stable matchings and the size of the core by means of maximal and average rank gaps. We provide upper bounds in terms of maximal and average disagreements in the agents’ rankings. Finally, we show that most of our bounds are tight.

Published as: The core of roommate problems: size and rank-fairness within matched pairs in International Journal of Game Theory , Vol. 48, No. 1, 157–179, March, 2019