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Stable matching with uncertain linear preferences

Stable matching with uncertain linear preferences
Stable matching with uncertain linear preferences
We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- for each agent, there is a probability distribution over linear preferences, (2) compact indifference model --- for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model --- there is a lottery over preference profiles.
For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists.
We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.
0178-4617
Aziz, Haris
ca1da602-f9b6-4d08-bd30-c822a1e2e54b
Biró, Péter
ec1199ef-3603-4075-ba20-2f388270894f
Gaspers, Serge
6f7b50ad-691c-43ce-8524-4ea948a47833
de Haan, Ronald
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Mattei, Nicholas
aa7f3dde-9378-4e94-be43-33c973fb8dec
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Aziz, Haris
ca1da602-f9b6-4d08-bd30-c822a1e2e54b
Biró, Péter
ec1199ef-3603-4075-ba20-2f388270894f
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, Gaspers, Serge, de Haan, Ronald, Mattei, Nicholas and Rastegari, Baharak (2019) Stable matching with uncertain linear preferences. Algorithmica. (doi:10.1007/s00453-019-00650-0).

Record type: Article

Abstract

We consider the two-sided stable matching setting in which there may be uncertainty about the agents' preferences due to limited information or communication. We consider three models of uncertainty: (1) lottery model --- for each agent, there is a probability distribution over linear preferences, (2) compact indifference model --- for each agent, a weak preference order is specified and each linear order compatible with the weak order is equally likely and (3) joint probability model --- there is a lottery over preference profiles.
For each of the models, we study the computational complexity of computing the stability probability of a given matching as well as finding a matching with the highest probability of being stable. We also examine more restricted problems such as deciding whether a certainly stable matching exists.
We find a rich complexity landscape for these problems, indicating that the form uncertainty takes is significant.

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More information

Accepted/In Press date: 27 October 2019
e-pub ahead of print date: 14 November 2019

Identifiers

Local EPrints ID: 435630
URI: http://eprints.soton.ac.uk/id/eprint/435630
ISSN: 0178-4617
PURE UUID: b5625904-ce0b-47af-87f6-19215fba776e
ORCID for Baharak Rastegari: ORCID iD orcid.org/0000-0002-0985-573X

Catalogue record

Date deposited: 14 Nov 2019 17:30
Last modified: 22 Nov 2021 03:23

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Contributors

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

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