Manipulation via Endowments in University-Admission Problem: Exogenously and Endogenously Determined Scholarships
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We consider a two-sided many-to-one matching model where universities offer scholarships to students. We show that every stable matching rule is manipulable by a university via destroying and predonating endowments under a fairly wide class of scholarship rules. We also show that the student- and university-optimal matching rules are non-manipulable under the class of scholarship rule, where the universities give some of their endowments only to their most preferred student as scholarship. Furthermore, we show that the set of Nash equilibria of the destruction game and the set of stable matchings may be disjoint. We also show that there exists a stable allocation which is manipulable by a university via destroying as well as via predonating endowments whenever the scholarships are determined endogenously in the model.
Abstract
We consider a two-sided many-to-one matching model where universities offer scholarships to students. We show that every stable matching rule is manipulable by a university via destroying and predonating endowments under a fairly wide class of scholarship rules. We also show that the student- and university-optimal matching rules are non-manipulable under the class of scholarship rule, where the universities give some of their endowments only to their most preferred student as scholarship. Furthermore, we show that the set of Nash equilibria of the destruction game and the set of stable matchings may be disjoint. We also show that there exists a stable allocation which is manipulable by a university via destroying as well as via predonating endowments whenever the scholarships are determined endogenously in the model.
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