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Some results on stability concepts for matching models

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2010-12
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Facultad de CC Económicas y Empresariales. Instituto Complutense de Análisis Económico
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We consider a general class of two-sided matching markets, called many-to-one matching markets with money. For a special case of these markets, where each seller owns di¤erent objects, we prove that stable outcomes cannot be characterized by the non-existence of unsatis…ed pairs. Moreover, we restore the dual lattice structure in markets with more than one seller using a connection with an assignment game.
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JEL Classification Numbers: C71, C78.
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Blair, C., 1988, The lattice structure of the set of stable matchings with multiple partners, Mathematical of Operations Research 13, 619-628. Camiña, E., 2006, A Generalized Assignment Game, Mathematical Social Sciences 52, 152-161. Martínez, R., Massó, J., Neme, A., Oviedo, J., 2001, On the lattice structure of the set of stable matchings for a many-to-one model, Optimization 50, 439-457. Roth, A., 1985, Conflict and coincidence of interest in job matching: some new results and open questions, Mathematics of Operations Research 10, 379-389. Sotomayor, M., 1992, The multiple partners game, in: M. Majumdar, Ed., Equilibrium and Dynamics: Essays in Honor to David Gale Macmillian, 322-336. Shapley, L. and M. Shubik, 1972, The assignment game I: the core, International Journal of Game Theory 1, 111-130.