Stable Matching with Multilayer Approval Preferences: Approvals Can Be Harder Than Strict Preferences

Matthias Bentert, Niclas Boehmer, Klaus Heeger, Tomohiro Koana

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study stable matching problems where agents have multilayer preferences: There are ℓ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC ’18] studied such problems with strict preferences, establishing four multilayer adaptations of classical notions of stability. We follow up on their work by analyzing the computational complexity of stable matching problems with multilayer approval preferences. We consider eleven stability notions derived from three well-established stability notions for stable matchings with ties and the four adaptations proposed by Chen et al. For each stability notion, we show that the problem of finding a stable matching is either polynomial-time solvable or NP-hard. Furthermore, we examine the influence of the number of layers and the desired “degree of stability” on the problems’ complexity. Somewhat surprisingly, we discover that assuming approval preferences instead of strict preferences does not considerably simplify the situation (and sometimes even makes polynomial-time solvable problems NP-hard).

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - 15th International Symposium, SAGT 2022, Proceedings
EditorsPanagiotis Kanellopoulos, Maria Kyropoulou, Alexandros Voudouris
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages18
ISBN (Print)9783031157134
StatePublished - 1 Jan 2022
Externally publishedYes
Event15th International Symposium on Algorithmic Game Theory, SAGT 2022 - Colchester, United Kingdom
Duration: 12 Sep 202215 Sep 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13584 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th International Symposium on Algorithmic Game Theory, SAGT 2022
Country/TerritoryUnited Kingdom

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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