TY - JOUR

T1 - Equilibria under deferred acceptance

T2 - Dropping strategies, filled positions, and welfare

AU - Jaramillo, Paula

AU - Kayi, Çaǧatay

AU - Klijn, Flip

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/11

Y1 - 2013/11

N2 - We study many-to-one matching markets where hospitals have responsive preferences over students. 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 equilibrium outcomes can be unstable. We prove that any stable matching is 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 '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 equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).

AB - We study many-to-one matching markets where hospitals have responsive preferences over students. 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 equilibrium outcomes can be unstable. We prove that any stable matching is 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 '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 equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).

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U2 - 10.1016/j.geb.2013.10.001

DO - 10.1016/j.geb.2013.10.001

M3 - Article

AN - SCOPUS:84887513539

SN - 0899-8256

VL - 82

SP - 693

EP - 701

JO - Games and Economic Behavior

JF - Games and Economic Behavior

ER -