"Farsighted Stability for Roommate Markets"
Harvard Business School NOM Unit Working Paper No. 09-135
BETTINA-ELISABETH KLAUS, Harvard Business School
FLIP KLIJN, Autonomous University of Barcelona - Department of Economics and Economic History
MARKUS WALZL, Department of Economics, Bamberg University
Using a bi-choice graph technique (Klaus and Klijn, 2009), we 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 (Proposition 1). Using this characterization of indirect dominance, we investigate von Neumann-Morgenstern farsightedly stable sets. We show that a singleton is von Neumann-Morgenstern farsightedly stable if and only if the matching is stable (Theorem 1). We also present roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set (Examples 1 and 2).