The core of roommate problems: size and rank-fairness within matched pairs

This paper deals with roommate problems (Gale and Shapley, Am Math Mon 69(1):9–15, 1962) that are solvable, i.e., have a non-empty core (set of stable matchings). We study rank-fairness within pairs 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.