Farsighted Stability for Roommate Markets

We study farsighted stability for roommate markets. 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 a roommate market without a von Neumann–Morgenstern farsightedly stable set (Example 1) and a roommate market with a nonsingleton von Neumann–Morgenstern farsightedly stable set (Example 2).