Stable Matching with Deviators and Conformists

[2601.18573] Stable Matching with Deviators and Conformists Skip to main content Search Submit Donate Log in Computer Science > Computer Science and Game Theory arXiv:2601.18573 (cs) [Submitted on 26 Jan 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Stable Matching with Deviators and Conformists Authors: Frederik Glitzner , Augustine Kwanashie , David Manlove View PDF HTML (experimental) Abstract: In the Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the Gale-Shapley algorithm, the existence of a stable matching is not guaranteed in the latter problem, but can be determined efficiently using Irving's algorithm. However, the computation of matchings that minimise the instability, either due to the presence of constraints on the size of the matching or due to restrictive preference cycles, gives rise to a collection of infamously intractable almost-stable matching problems. In practice, however, not every agent is able or likely to initiate deviations caused by blocking pairs. Suppose we knew, for example, due to a set of requirements or estimates based on historical data, which agents are likely to initiate deviations - the deviators - and which are likely to comply with whatever matching they are presented with - the conformists. Can we decide efficiently whether a matching exists in which no deviator is blocking, i.e., in which no deviator has an incentive to initiate a deviation? Furthermore, can we find matchings in which only a few deviators are blocking? We characterise the computational complexity of this question in bipartite and non-bipartite settings. Surprisingly, these problems prove intractable in very strong ways. On the positive side, we identify polynomial-time and fixed-parameter tractable cases (with respect to the number of deviators and the preference list length), providing novel algorithmics for problems where stability cannot be fully guaranteed, and resolving some open cases from the literature along the way. Subjects: Computer Science and Game Theory (cs.GT) ; Data Structures and Algorithms (cs.DS) Cite as: arXiv:2601.18573 [cs.GT] (or arXiv:2601.18573v2 [cs.GT] for this version) https://doi.org/10.48550/arXiv.2601.18573 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Frederik Glitzner [ view email ] [v1] Mon, 26 Jan 2026 15:16:15 UTC (440 KB) [v2] Tue, 25 Aug 2026 09:17:13 UTC (350 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.GT < prev | next > new | recent | 2026-01 Change to browse by: cs cs.DS References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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