Farsighted Stability For Roommate Markets

Using a bi-choice graph technique, the authors show that a matching for a roommate market indirectly dominates another matching if and only if no blocking pair of the former is matched in the latter. Using this characterization of indirect dominance, they investigate von Neumann-Morgenstern farsightedly stable sets. They show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable. They also present roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set