[2608.14461] Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Computer Science and Game Theory arXiv:2608.14461 (cs) [Submitted on 14 Aug 2026 ( v1 ), last revised 30 Aug 2026 (this version, v2)] Title: Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals Authors: Šimon Schierreich , Ildikó Schlotter View a PDF of the paper titled Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals, by \v{S}imon Schierreich and Ildik\'o Schlotter View PDF HTML (experimental) Abstract: We study constrained coalition formation in games induced by friends, enemies, and neutrals, under the two standard refinements of additively separable preferences: friend-oriented and enemy-oriented. We ask for partitions that are individually rational (IR), while additionally requiring exactly $k$ non-empty coalitions, each satisfying a prescribed lower and upper bound on its size. Although IR alone is trivial to satisfy for any hedonic game, the size constraints make it computationally intractable to decide whether a feasible partition exists. The two models tell strikingly different stories. Under enemy-oriented preferences, the problem collapses to size-constrained graph coloring, and its complexity follows accordingly. Under friend-oriented preferences, however, the picture is far more intricate, and is governed by the enmity structure rather than the friendships. The complexity is further shaped by two factors: how strict the imposed size requirements are, and whether relationships are symmetric or asymmetric, with several cases turning out tractable in the symmetric setting but intractable once asymmetry is allowed. Charting this boundary in terms of both classical and parameterized complexity, we provide a complete understanding of which properties of the friend/enemy structure are responsible for hardness. Subjects: Computer Science and Game Theory (cs.GT) Cite as: arXiv:2608.14461 [cs.GT] (or arXiv:2608.14461v2 [cs.GT] for this version) https://doi.org/10.48550/arXiv.2608.14461 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ildikó Schlotter [ view email ] [v1] Fri, 14 Aug 2026 16:42:52 UTC (71 KB) [v2] Sun, 30 Aug 2026 14:29:07 UTC (71 KB) Full-text links: Access Paper: View a PDF of the paper titled Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals, by \v{S}imon Schierreich and Ildik\'o Schlotter View PDF HTML (experimental) TeX Source view license Current browse context: cs.GT < prev | next > new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from