research-article

Reasoning about optimal stable matchings under partial information

Authors:

Baharak Rastegari,

Nicole Immorlica,

Kevin Leyton-BrownAuthors Info & Claims

EC '14: Proceedings of the fifteenth ACM conference on Economics and computation

Pages 431 - 448

https://doi.org/10.1145/2600057.2602884

Published: 01 June 2014 Publication History

Abstract

We study two-sided matching markets in which participants are initially endowed with partial preference orderings, lacking precise information about their true, strictly ordered list of preferences. We wish to reason about matchings that are stable with respect to agents' true preferences, and which are furthermore optimal for one given side of the market. We present three main results. First, one can decide in polynomial time whether there exists a matching that is stable and optimal under all strict preference orders that refine the given partial orders, and can construct this matching in polynomial time if it does exist. We show, however, that deciding whether a given pair of agents are matched in all or no such optimal stable matchings is co-NP-complete, even under quite severe restrictions on preferences. Finally, we describe a polynomial-time algorithm that decides, given a matching that is stable under the partial preference orderings, whether that matching is stable and optimal for one side of the market under some refinement of the partial orders.

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Cited By

Chu YLuo JZheng T(2024)Stable Matching with Approval Preferences Under Partial InformationAlgorithmic Aspects in Information and Management10.1007/978-981-97-7801-0_6(64-75)Online publication date: 19-Sep-2024
https://doi.org/10.1007/978-981-97-7801-0_6
Chen YHu G(2023)A Theory of Stability in Matching with Incomplete InformationAmerican Economic Journal: Microeconomics10.1257/mic.2020041115:1(288-322)Online publication date: 1-Feb-2023
https://doi.org/10.1257/mic.20200411
Houhamdi ZAthamena BElRefae G(2022)Two-Sided Matching Under Incomplete Information2022 International Arab Conference on Information Technology (ACIT)10.1109/ACIT57182.2022.9994171(1-6)Online publication date: 22-Nov-2022
https://doi.org/10.1109/ACIT57182.2022.9994171
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Index Terms

Reasoning about optimal stable matchings under partial information
1. Applied computing
  1. Law, social and behavioral sciences
    1. Economics

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cover image ACM Conferences

EC '14: Proceedings of the fifteenth ACM conference on Economics and computation

June 2014

1028 pages

ISBN:9781450325653

DOI:10.1145/2600057

General Chair:
Moshe Babaioff
Microsoft Research
,
Program Chairs:
Vincent Conitzer
Duke University
,
David Easley
Cornell University

Copyright © 2014 ACM.

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Published: 01 June 2014

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EC '14: ACM Conference on Economics and Computation

June 8 - 12, 2014

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Cited By

Chu YLuo JZheng T(2024)Stable Matching with Approval Preferences Under Partial InformationAlgorithmic Aspects in Information and Management10.1007/978-981-97-7801-0_6(64-75)Online publication date: 19-Sep-2024
https://doi.org/10.1007/978-981-97-7801-0_6
Chen YHu G(2023)A Theory of Stability in Matching with Incomplete InformationAmerican Economic Journal: Microeconomics10.1257/mic.2020041115:1(288-322)Online publication date: 1-Feb-2023
https://doi.org/10.1257/mic.20200411
Houhamdi ZAthamena BElRefae G(2022)Two-Sided Matching Under Incomplete Information2022 International Arab Conference on Information Technology (ACIT)10.1109/ACIT57182.2022.9994171(1-6)Online publication date: 22-Nov-2022
https://doi.org/10.1109/ACIT57182.2022.9994171
Aziz HBiró PFleiner TGaspers Sde Haan RMattei NRastegari B(2022)Stable Matching with Uncertain Pairwise PreferencesTheoretical Computer Science10.1016/j.tcs.2022.01.028Online publication date: Jan-2022
https://doi.org/10.1016/j.tcs.2022.01.028
Todo TWada RYahiro KYokoo M(2021)Lazy Gale-Shapley for Many-to-One Matching with Partial InformationAlgorithmic Decision Theory10.1007/978-3-030-87756-9_25(390-405)Online publication date: 27-Oct-2021
https://doi.org/10.1007/978-3-030-87756-9_25
Cechlárová KGourvès LLesca J(2019)On the problem of assigning PhD grantsProceedings of the 28th International Joint Conference on Artificial Intelligence10.5555/3367032.3367052(130-136)Online publication date: 10-Aug-2019
https://dl.acm.org/doi/10.5555/3367032.3367052
Aziz HBiró Pde Haan RRastegari B(2019)Pareto Optimal Allocation under Uncertain Preferences: Uncertainty Models, Algorithms, and ComplexityArtificial Intelligence10.1016/j.artint.2019.08.002Online publication date: Aug-2019
https://doi.org/10.1016/j.artint.2019.08.002
Aziz HBiró PGaspers Sde Haan RMattei NRastegari B(2019)Stable Matching with Uncertain Linear PreferencesAlgorithmica10.1007/s00453-019-00650-0Online publication date: 14-Nov-2019
https://doi.org/10.1007/s00453-019-00650-0
Menon VLarson K(2018)Robust and Approximately Stable Marriages Under Partial InformationWeb and Internet Economics10.1007/978-3-030-04612-5_23(341-355)Online publication date: 21-Nov-2018
https://doi.org/10.1007/978-3-030-04612-5_23
Aziz HDe Haan RRastegari B(2017)Pareto optimal allocation under uncertain preferencesProceedings of the 26th International Joint Conference on Artificial Intelligence10.5555/3171642.3171655(77-83)Online publication date: 19-Aug-2017
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