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Stable matching with uncertain pairwise preferences

Stable matching with uncertain pairwise preferences
Stable matching with uncertain pairwise preferences
We study a two-sided matching problem under preferences, where the agents have independent pairwise comparisons on their possible partners and these preferences may be uncertain. Preferences may be intransitive and agents may even have cycles in their preferences; e.g. an agent a may prefer b to c, c to d, and d to b, all with probability one. If an instance has such a cycle, then there may not exist any matching that is stable with positive probability. We focus on the computational problems of checking the existence of possibly and certainly stable matchings, i.e., matchings whose probability of being stable is positive or one, respectively. We show that finding possibly stable matchings is NP-hard, even if only one side can have cyclic preferences. On the other hand we show that the problem of finding a certainly stable matching is polynomial-time solvable if only one side can have cyclic preferences and the other side has transitive preferences, but that this problem becomes NP-hard when both sides can have cyclic preferences.
two-sided matching, stability, uncertain preferences
0304-3975
1-11
Aziz, Haris
ca1da602-f9b6-4d08-bd30-c822a1e2e54b
Biró, Péter
ec1199ef-3603-4075-ba20-2f388270894f
Fleiner, Tamás
214379f3-ab43-49f4-861c-427ba26effe0
Gaspers, Serge
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de Haan, Ronald
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Mattei, Nicholas
aa7f3dde-9378-4e94-be43-33c973fb8dec
Rastegari, Baharak
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Aziz, Haris
ca1da602-f9b6-4d08-bd30-c822a1e2e54b
Biró, Péter
ec1199ef-3603-4075-ba20-2f388270894f
Fleiner, Tamás
214379f3-ab43-49f4-861c-427ba26effe0
Gaspers, Serge
6f7b50ad-691c-43ce-8524-4ea948a47833
de Haan, Ronald
2d29a3e0-f335-4cdf-a62b-c1c293283839
Mattei, Nicholas
aa7f3dde-9378-4e94-be43-33c973fb8dec
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1

Aziz, Haris, Biró, Péter, Fleiner, Tamás, Gaspers, Serge, de Haan, Ronald, Mattei, Nicholas and Rastegari, Baharak (2022) Stable matching with uncertain pairwise preferences. Theoretical Computer Science, 909, 1-11. (doi:10.1016/j.tcs.2022.01.028).

Record type: Article

Abstract

We study a two-sided matching problem under preferences, where the agents have independent pairwise comparisons on their possible partners and these preferences may be uncertain. Preferences may be intransitive and agents may even have cycles in their preferences; e.g. an agent a may prefer b to c, c to d, and d to b, all with probability one. If an instance has such a cycle, then there may not exist any matching that is stable with positive probability. We focus on the computational problems of checking the existence of possibly and certainly stable matchings, i.e., matchings whose probability of being stable is positive or one, respectively. We show that finding possibly stable matchings is NP-hard, even if only one side can have cyclic preferences. On the other hand we show that the problem of finding a certainly stable matching is polynomial-time solvable if only one side can have cyclic preferences and the other side has transitive preferences, but that this problem becomes NP-hard when both sides can have cyclic preferences.

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Accepted/In Press date: 2022
Published date: 28 March 2022
Additional Information: Funding Information: Biró gratefully acknowledges financial support from the Hungarian Scientific Research Fund, OTKA , Grant No. K128611 , and the Hungarian Academy of Sciences , Momentum Grant No. LP2021-2 . Ronald de Haan was supported by the Austrian Science Fund (FWF), project J4047 . Rastegari was supported EPSRC grant EP/K010042/1 at the time of the submission. The authors gratefully acknowledge the support from European Cooperation in Science and Technology (COST) action IC1205 . Nicholas Mattei was supported by NSF (National Science Foundation) Award IIS-2007955 during a portion of this project. Publisher Copyright: © 2022 Elsevier B.V. Copyright: Copyright 2022 Elsevier B.V., All rights reserved.
Keywords: two-sided matching, stability, uncertain preferences

Identifiers

Local EPrints ID: 454804
URI: http://eprints.soton.ac.uk/id/eprint/454804
ISSN: 0304-3975
PURE UUID: 77ecf3be-fe19-4807-b3f2-49b016f0e86b
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

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Date deposited: 24 Feb 2022 21:44
Last modified: 25 Jan 2023 02:59

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Contributors

Author: Haris Aziz
Author: Péter Biró
Author: Tamás Fleiner
Author: Serge Gaspers
Author: Ronald de Haan
Author: Nicholas Mattei
Author: Baharak Rastegari ORCID iD

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