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Farsighted Stability for Roommate Markets

Authors


  • Bettina Klaus, Faculty of Business and Economics, University of Lausanne, Internef 538, CH-1015 Lausanne, Switzerland (bettina.klaus@unil.ch). Flip Klijn, Institute for Economic Analysis (CSIC), Campus UAB, 08193 Bellaterra (Barcelona), Spain (flip.klijn@iae.csic.es). Markus Walzl, Department of Economics, Innsbruck University, Universitätsstraße 15, 6020 Innsbruck, Austria (markus.walzl@uibk.ac.at).

  •  We thank three referees for very useful comments and suggestions. B. Klaus thanks the Netherlands Organization for Scientific Research (NWO) for its support under grant VIDI-452-06-013. F. Klijn gratefully acknowledges the support from Plan Nacional I+D+i (ECO2008–04784), the Consolider-Ingenio 2010 (CSD2006–00016) program, the Barcelona Graduate School of Economics and the Government of Catalonia (SGR2009–01142).

Abstract

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).

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