von Neumann-Morgenstern farsightedly stable sets in two-sided matching

Abstract

We adopt the notion of vonNeumann–Morgenstern (vNM) farsightedly stable sets\nto determine which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of vNMfarsightedly stable sets: a set of matchings is a vNM farsightedly stable set if and only if it is a singleton subset of the core. Thus, contrary to the vNM (myopically) stable sets (Ehlers 2007), vNM farsightedly stable sets cannot include matchings that are not in the core. Moreover, we show that our main result is robust to many-to-one matching problems with substitutable preferences: a set of matchings is a vNM farsightedly stable set if and only if it is a singleton set and its element is in the strong core.