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

Ana Mauleon, Vincent J. Vannetelbosch, Wouter Vergote

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.

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Year of publication:	September 2011
Authors:	Mauleon, Ana ; Vannetelbosch, Vincent J. ; Vergote, Wouter
Published in:	Theoretical economics : TE ; an open access journal in economic theory. - Toronto : [Verlag nicht ermittelbar], ISSN 1555-7561, ZDB-ID 2220447-7. - Vol. 6.2011, 3, p. 499-521
Subject:	Matching problem \| von Neumann-Morgenstern stable sets \| farsighted stability \| Core \| Matching \| Kooperatives Spiel \| Cooperative game \| Spieltheorie \| Game theory