Equilibria Under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare (Equilibrios bajo el mecanismo de aceptaci´on diferida: Estrategias de eliminaci´on, posiciones ocupadas y bienestar)

20 Pages Posted: 9 May 2013

See all articles by Paula Jaramillo

Paula Jaramillo

Universidad de los Andes, Colombia - Department of Economics

Cagatay Kayi

Universidad del Rosario

Flip Klijn

Autonomous University of Barcelona - Department of Economics and Economic History

Date Written: April 18, 2013

Abstract

This paper studies many-to-one matching markets where each student is assigned to a hospital. Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling.

Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the so-called 'rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospital-optimal stable matchings (with respect to the true preferences).

Keywords: many- to-one matching, deferred acceptance, Nash equilibrium, dropping strategies, filled positions, welfare

JEL Classification: C78, D60

Suggested Citation

Jaramillo, Paula and Kayi, Cagatay and Klijn, Flip, Equilibria Under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare (Equilibrios bajo el mecanismo de aceptaci´on diferida: Estrategias de eliminaci´on, posiciones ocupadas y bienestar) (April 18, 2013). Documento CEDE No. 2013-23, Available at SSRN: https://ssrn.com/abstract=2262356 or http://dx.doi.org/10.2139/ssrn.2262356

Paula Jaramillo (Contact Author)

Universidad de los Andes, Colombia - Department of Economics ( email )

Carrera 1a No. 18A-10
Santafe de Bogota, AA4976
Colombia

Cagatay Kayi

Universidad del Rosario ( email )

Calle 12 No. 6-25
Bogota, DC
Colombia

Flip Klijn

Autonomous University of Barcelona - Department of Economics and Economic History ( email )

Edifici B - Campus Bellaterra
Barcelona, 08193
Spain

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