Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences
Abstract
The aim of this paper is to propose a new solution
for the roommate problem with strict
references. We introduce the solution of maximum ir
reversibility and consider almost stable
matchings (Abraham et al. [2]) and maximum stable m
atchings (Tan [30] [32]). We find that
almost stable matchings are incompatible with the o
ther two solutions. Hence, to solve the
roommate problem we propose matchings that lie at t
he intersection of the maximum
irreversible matchings and maximum stable matchings
, which are called Q-stable matchings.
These matchings are core consistent and we offer an
efficient algorithm for computing one of
them. The outcome of the algorithm belongs to an ab
sorbing set
