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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.
0302-9743
27-39
Springer
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 F.
f4a5d0ae-193e-49e1-a14a-a471ce74d877
Mourtos, Ioannis
629eda2b-8129-42fd-b496-d1b883174258
Oceľáková, Eva
7bddd98a-ef68-4fd7-9512-42fbd6d8df80
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Hoefer, M.
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 F.
f4a5d0ae-193e-49e1-a14a-a471ce74d877
Mourtos, Ioannis
629eda2b-8129-42fd-b496-d1b883174258
Oceľáková, Eva
7bddd98a-ef68-4fd7-9512-42fbd6d8df80
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Hoefer, M.

Cechlárová, Katarína, Eirinakis, Pavlos, Fleiner, Tamás, Magos, Dimitrios, Manlove, David F., Mourtos, Ioannis, Oceľáková, Eva and Rastegari, Baharak (2015) Pareto optimal matchings in many-to-many markets with ties. In, Hoefer, M. (ed.) Lecture Notes in Computer Science. (Algorithmic Game Theory, , (doi:10.1007/978-3-662-48433-3_3), 9347) Berlin; Heidelberg. Springer, pp. 27-39. (doi:10.1007/978-3-662-48433-3_3).

Record type: Book Section

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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Published date: 10 December 2015

Identifiers

Local EPrints ID: 426211
URI: https://eprints.soton.ac.uk/id/eprint/426211
ISSN: 0302-9743
PURE UUID: c3df6145-0c0d-4ddf-aa7f-36aed51eba48
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: 14 Mar 2019 01:20

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Contributors

Author: Katarína Cechlárová
Author: Pavlos Eirinakis
Author: Tamás Fleiner
Author: Dimitrios Magos
Author: David F. Manlove
Author: Ioannis Mourtos
Author: Eva Oceľáková
Author: Baharak Rastegari ORCID iD
Editor: M. Hoefer

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