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Wednesday, June 24, 2009

Good thing I don't need a roommate

I am SO glad I'm married. Otherwise, I might be looking for a roommate. This paper from the Harvard Business School makes this sound complicated:

"Farsighted Stability for Roommate Markets"
Harvard Business School NOM Unit Working Paper No. 09-135

BETTINA-ELISABETH KLAUS, Harvard Business School
Email: bklaus@hbs.edu
FLIP KLIJN, Autonomous University of Barcelona - Department of Economics and Economic History
Email: fklijn@pareto.uab.es
MARKUS WALZL, Department of Economics, Bamberg University
Email: markus.walzl@uni-bamberg.de

Using a bi-choice graph technique (Klaus and Klijn, 2009), 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 roommate markets with no and with a non-singleton von Neumann-Morgenstern farsightedly stable set (Examples 1 and 2).