Absolutely Stable Roommate Problems

Different solution concepts (core, stable sets, largest consistent set, ...) can be defined using either a direct or an indirect dominance relation. Direct dominance implies indirect dominance, but not the reverse. Hence, the predicted outcomes when assuming myopic (direct) or farsighted (indirect) agents could be very different. In this paper, we characterize absolutely stable roommate problems when preferences are strict. That is, we obtain the conditions on preference profiles such that indirect dominance implies direct dominance in roommate problems. Furthermore, we characterize absolutely stable roommate problems having a non-empty core. Finally, we show that, if the core of an absolutely stable roommate problem is not empty, it contains a unique matching in which all agents who mutually top rank each other are matched to one another and all other agents remain unmatched.