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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 — in which 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.
1611-3349
195-206
Springer
Aziz, Haris
99c295f2-f10c-4e8e-b48c-3f4048a075f3
Biró, Péter
ec1199ef-3603-4075-ba20-2f388270894f
Gaspers, Serge
a36a2ff6-0172-4925-bc3b-3ff1de75c6c3
De Haan, Ronald
2d29a3e0-f335-4cdf-a62b-c1c293283839
Mattei, Nicholas
00469787-b1ab-47d3-9b75-40eccca44ee3
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Gairing, M.
Savani, R.
Aziz, Haris
99c295f2-f10c-4e8e-b48c-3f4048a075f3
Biró, Péter
ec1199ef-3603-4075-ba20-2f388270894f
Gaspers, Serge
a36a2ff6-0172-4925-bc3b-3ff1de75c6c3
De Haan, Ronald
2d29a3e0-f335-4cdf-a62b-c1c293283839
Mattei, Nicholas
00469787-b1ab-47d3-9b75-40eccca44ee3
Rastegari, Baharak
6ba9e93c-53ba-4090-8f77-c1cb1568d7d1
Gairing, M.
Savani, R.

Aziz, Haris, Biró, Péter, Gaspers, Serge, De Haan, Ronald, Mattei, Nicholas and Rastegari, Baharak (2016) Stable matching with uncertain linear preferences. In, Gairing, M. and Savani, R. (eds.) Lecture Notes in Computer Science. (Algorithmic Game Theory. SAGT 2016, , (doi:10.1007/978-3-662-53354-3_16), 9928) Berlin; Heidelberg. Springer, pp. 195-206. (doi:10.1007/978-3-662-53354-3_16).

Record type: Book Section

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 — in which 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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e-pub ahead of print date: 1 September 2016
Published date: 1 September 2016

Identifiers

Local EPrints ID: 426214
URI: https://eprints.soton.ac.uk/id/eprint/426214
ISSN: 1611-3349
PURE UUID: 46ba4d4d-b899-4d3d-98cd-653668e2dc79
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: 15 Aug 2019 00:21

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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
Editor: M. Gairing
Editor: R. Savani

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