research-article

Matchings under Preferences: Strength of Stability and Tradeoffs

Authors:

Manuel SorgeAuthors Info & Claims

ACM Transactions on Economics and Computation, Volume 9, Issue 4

Article No.: 20, Pages 1 - 55

https://doi.org/10.1145/3485000

Published: 16 October 2021 Publication History

Abstract

We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classical sense, even if the agents slightly change their preferences. Near stability, however, imposes that a matching must become stable (again, in the classical sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of tradeoffs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined tradeoffs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching (if it exists), and we prove that finding a socially optimal and nearly stable matching is computationally hard.

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Cited By

Yang YMöhring RSong JXu YZhang Y(2025)ILP-Based Heuristics for the Multi-Modal Stable Matching ProblemTsinghua Science and Technology10.26599/TST.2023.901013530:2(479-487)Online publication date: Apr-2025
https://doi.org/10.26599/TST.2023.9010135
Csáji GDastani MSichman JAlechina NDignum V(2024)A Simple 1.5-approximation Algorithm for a Wide Range of Maximum Size Stable Matching ProblemsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662890(409-415)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662890
Csáji GLarson K(2024)Popular and dominant matchings with uncertain and multimodal preferencesProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/303(2740-2747)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/303
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Index Terms

Matchings under Preferences: Strength of Stability and Tradeoffs
1. Theory of computation

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Published In

cover image ACM Transactions on Economics and Computation

ACM Transactions on Economics and Computation Volume 9, Issue 4

December 2021

202 pages

ISSN:2167-8375

EISSN:2167-8383

DOI:10.1145/3485144

Editors:
David Pennock
Microsoft, USA
,
Ilya Segal
Stanford University, USA

Issue’s Table of Contents

Copyright © 2021 Association for Computing Machinery.

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Publication History

Published: 16 October 2021

Accepted: 01 April 2021

Revised: 01 March 2021

Received: 01 July 2019

Published in TEAC Volume 9, Issue 4

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Cited By

Yang YMöhring RSong JXu YZhang Y(2025)ILP-Based Heuristics for the Multi-Modal Stable Matching ProblemTsinghua Science and Technology10.26599/TST.2023.901013530:2(479-487)Online publication date: Apr-2025
https://doi.org/10.26599/TST.2023.9010135
Csáji GDastani MSichman JAlechina NDignum V(2024)A Simple 1.5-approximation Algorithm for a Wide Range of Maximum Size Stable Matching ProblemsProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662890(409-415)Online publication date: 6-May-2024
https://dl.acm.org/doi/10.5555/3635637.3662890
Csáji GLarson K(2024)Popular and dominant matchings with uncertain and multimodal preferencesProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence10.24963/ijcai.2024/303(2740-2747)Online publication date: 3-Aug-2024
https://dl.acm.org/doi/10.24963/ijcai.2024/303
Schlotter I(2024)Recognizing when a preference system is close to admitting a master listTheoretical Computer Science10.1016/j.tcs.2024.114445994:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.tcs.2024.114445
Bérczi KCsáji GKirály T(2024)Manipulating the outcome of stable marriage and roommates problemsGames and Economic Behavior10.1016/j.geb.2024.08.010Online publication date: Aug-2024
https://doi.org/10.1016/j.geb.2024.08.010
Kreisel LBoehmer NFroese VNiedermeier R(2024)Equilibria in schelling games: computational hardness and robustnessAutonomous Agents and Multi-Agent Systems10.1007/s10458-023-09632-738:1Online publication date: 1-Jun-2024
https://dl.acm.org/doi/10.1007/s10458-023-09632-7
Alimudin AIshida YSuzuki K(2023)Maintaining Stability for a Matching Problem Under Dynamic PreferenceIEEE Access10.1109/ACCESS.2023.324324511(24203-24215)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3243245
Eiben EGutin GNeary PRambaud CWahlström MYeo A(2023)Preference swaps for the stable matching problemTheoretical Computer Science10.1016/j.tcs.2022.11.003940:PA(222-230)Online publication date: 9-Jan-2023
https://dl.acm.org/doi/10.1016/j.tcs.2022.11.003
Bampis EEscoffier BYoussef P(2023)Online 2-stage stable matchingDiscrete Applied Mathematics10.1016/j.dam.2023.09.009341:C(394-405)Online publication date: 31-Dec-2023
https://dl.acm.org/doi/10.1016/j.dam.2023.09.009
Schlotter I(2023)Recognizing When a Preference System is Close to Admitting a Master ListWALCOM: Algorithms and Computation10.1007/978-3-031-27051-2_27(317-329)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/978-3-031-27051-2_27
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