Finding a stable matching under type-specific minimum quotas

Tomoeda, K

Finding a stable matching under type-specific minimum quotas

Tomoeda, K

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Publication Type:: Journal Article
Citation:: Journal of Economic Theory, 2018, 176 pp. 81 - 117
Issue Date:: 2018-07-01

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Field	Value	Language
dc.contributor.author	Tomoeda, K https://orcid.org/0000-0001-6236-7439	en_US
dc.date.available	2020-07-01T19:05:13Z
dc.date.issued	2018-07-01	en_US
dc.identifier.citation	Journal of Economic Theory, 2018, 176 pp. 81 - 117	en_US
dc.identifier.issn	0022-0531	en_US
dc.identifier.uri	http://hdl.handle.net/10453/127681
dc.description.abstract	© 2018 Elsevier Inc. In matching problems with minimum and maximum type-specific quotas, there may not exist a stable (i.e., fair and non-wasteful) assignment (Ehlers et al., 2014). This paper investigates the structure of schools’ priority rankings which guarantees stability. First, we show that there always exists a fair and non-wasteful assignment if for each type of students, schools have common priority rankings over a certain number of bottom students. Next, we show that the pairwise version of this condition characterizes the maximal domain of two schools’ priority rankings over same type students to guarantee the existence of stable assignments. To prove the existence theorem, we propose a new mechanism Deferred Acceptance with Precedence Lists (DAPL), which is feasible, non-wasteful, strictly PL-fair and group strategy-proof for any priority rankings. Strict PL-fairness is weaker than fairness, but DAPL satisfies fairness under our sufficient condition. We also show that there is no strategy-proof mechanism that Pareto dominates DAPL whenever the outcome of DAPL is Pareto dominated by a stable assignment.	en_US
dc.relation.ispartof	Journal of Economic Theory	en_US
dc.relation.isbasedon	10.1016/j.jet.2018.03.008	en_US
dc.subject.classification	Economic Theory	en_US
dc.title	Finding a stable matching under type-specific minimum quotas	en_US
dc.type	Journal Article
utslib.citation.volume	176	en_US
utslib.for	1401 Economic Theory	en_US
utslib.for	1499 Other Economics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
pubs.organisational-group	/University of Technology Sydney/Faculty of Business/Economics Discipline
utslib.copyright.status	open_access	*
pubs.publication-status	Published	en_US
pubs.volume	176	en_US

Abstract:

© 2018 Elsevier Inc. In matching problems with minimum and maximum type-specific quotas, there may not exist a stable (i.e., fair and non-wasteful) assignment (Ehlers et al., 2014). This paper investigates the structure of schools’ priority rankings which guarantees stability. First, we show that there always exists a fair and non-wasteful assignment if for each type of students, schools have common priority rankings over a certain number of bottom students. Next, we show that the pairwise version of this condition characterizes the maximal domain of two schools’ priority rankings over same type students to guarantee the existence of stable assignments. To prove the existence theorem, we propose a new mechanism Deferred Acceptance with Precedence Lists (DAPL), which is feasible, non-wasteful, strictly PL-fair and group strategy-proof for any priority rankings. Strict PL-fairness is weaker than fairness, but DAPL satisfies fairness under our sufficient condition. We also show that there is no strategy-proof mechanism that Pareto dominates DAPL whenever the outcome of DAPL is Pareto dominated by a stable assignment.

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http://hdl.handle.net/10453/127681