Farsighted Stability for Roommate Markets

• Authors: Flip Klijn.
• BSE Working Paper: 385 | September 15
• Keywords: core , roommate markets , farsighted stability , one- and two-sided matching , von Neumann-Morgenstern stability
• JEL codes: C62, C71, C78
• core
• roommate markets
• farsighted stability
• one- and two-sided matching
• von Neumann-Morgenstern stability

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).