Theoretical Economics 6 (2011), 499–521

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### Von Neumann-Morgenstern farsightedly stable sets in two-sided matching

*Ana Mauleon, Vincent J. Vannetelbosch, Wouter Vergote*

#### Abstract

We adopt the notion of von Neumann-Morgenstern (vNM) farsightedly stable sets to determine which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of vNM farsightedly 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, J. of Econ. Theory 134 (2007), 537-547], 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.

Keywords: Matching problem, von Neumann-Morgenstern stable sets, farsighted stability

JEL classification: C70, C78

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