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Pareto optimal matchings in many-to-many markets with ties

Pareto optimal matchings in many-to-many markets with ties
Pareto optimal matchings in many-to-many markets with ties
We consider Pareto optimal matchings (POMs) in a many-to-many market of applicants and courses where applicants have preferences, which may include ties, over individual courses and lexicographic preferences over sets of courses. Since this is the most general setting examined so far in the literature, our work unifies and generalizes several known results. Specifically, we characterize POMs and introduce the Generalized Serial Dictatorship Mechanism with Ties (GSDT) that effectively handles ties via properties of network flows. We show that GSDT can generate all POMs using different priority orderings over the applicants, but it satisfies truthfulness only for certain such orderings. This shortcoming is not specific to our mechanism; we show that any mechanism generating all POMs in our setting is prone to strategic manipulation. This is in contrast to the one-to-one case (with or without ties), for which truthful mechanisms generating all POMs do exist.
1432-4350
700-721
Cechlárová, Katarína
5321a2f2-4a83-4550-b285-75e34e596864
Eirinakis, Pavlos
1946d86d-80f7-4ff8-9bb4-ad6953111cd1
Fleiner, Tamás
214379f3-ab43-49f4-861c-427ba26effe0
Magos, Dimitrios
4d4c5bc1-221c-47a0-a5dc-9c8ee8e069ca
Manlove, David
a4321a32-3611-4a9f-9dfe-c595dc7a5a38
Mourtos, Ioannis
629eda2b-8129-42fd-b496-d1b883174258
Ocel̆áková, Eva
11c34374-50c4-487b-ab9f-5e1299ca461a
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Cechlárová, Katarína
5321a2f2-4a83-4550-b285-75e34e596864
Eirinakis, Pavlos
1946d86d-80f7-4ff8-9bb4-ad6953111cd1
Fleiner, Tamás
214379f3-ab43-49f4-861c-427ba26effe0
Magos, Dimitrios
4d4c5bc1-221c-47a0-a5dc-9c8ee8e069ca
Manlove, David
a4321a32-3611-4a9f-9dfe-c595dc7a5a38
Mourtos, Ioannis
629eda2b-8129-42fd-b496-d1b883174258
Ocel̆áková, Eva
11c34374-50c4-487b-ab9f-5e1299ca461a
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1

Cechlárová, Katarína, Eirinakis, Pavlos, Fleiner, Tamás, Magos, Dimitrios, Manlove, David, Mourtos, Ioannis, Ocel̆áková, Eva and Rastegari, Baharak (2016) Pareto optimal matchings in many-to-many markets with ties. Theory of Computing Systems, 59 (4), 700-721. (doi:10.1007/s00224-016-9677-1).

Record type: Article

Abstract

We consider Pareto optimal matchings (POMs) in a many-to-many market of applicants and courses where applicants have preferences, which may include ties, over individual courses and lexicographic preferences over sets of courses. Since this is the most general setting examined so far in the literature, our work unifies and generalizes several known results. Specifically, we characterize POMs and introduce the Generalized Serial Dictatorship Mechanism with Ties (GSDT) that effectively handles ties via properties of network flows. We show that GSDT can generate all POMs using different priority orderings over the applicants, but it satisfies truthfulness only for certain such orderings. This shortcoming is not specific to our mechanism; we show that any mechanism generating all POMs in our setting is prone to strategic manipulation. This is in contrast to the one-to-one case (with or without ties), for which truthful mechanisms generating all POMs do exist.

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Cechlárová 2016 Article Pareto Optimal Matchings In Many - Version of Record
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e-pub ahead of print date: 30 April 2016
Published date: 1 November 2016

Identifiers

Local EPrints ID: 426215
URI: http://eprints.soton.ac.uk/id/eprint/426215
ISSN: 1432-4350
PURE UUID: ea899753-c967-4519-9ddb-c4a7fedc4c40
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

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Date deposited: 19 Nov 2018 17:30
Last modified: 03 Dec 2019 01:22

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Contributors

Author: Katarína Cechlárová
Author: Pavlos Eirinakis
Author: Tamás Fleiner
Author: Dimitrios Magos
Author: David Manlove
Author: Ioannis Mourtos
Author: Eva Ocel̆áková
Author: Baharak Rastegari ORCID iD

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