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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2023.41
URN: urn:nbn:de:0030-drops-185759
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18575/
Demeulemeester, Tom ;
Peters, Jannik
Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities
Abstract
We study relationships between different relaxed notions of core stability in hedonic games. In particular, we study (i) q-size core stable outcomes in which no deviating coalition of size at most q exists and (ii) k-improvement core stable outcomes in which no coalition can improve by a factor of more than k. For a large class of hedonic games, including fractional and additively separable hedonic games, we derive upper bounds on the maximum factor by which a coalition of a certain size can improve in a q-size core stable outcome. We further provide asymptotically tight lower bounds for a large class of hedonic games. Finally, our bounds allow us to confirm two conjectures by Fanelli et al. [Angelo Fanelli et al., 2021][IJCAI'21] for symmetric fractional hedonic games (S-FHGs): (i) every q-size core stable outcome in an S-FHG is also q/(q-1)-improvement core stable and (ii) the price of anarchy of q-size stability in S-FHGs is precisely 2q/q-1.
BibTeX - Entry
@InProceedings{demeulemeester_et_al:LIPIcs.MFCS.2023.41,
author = {Demeulemeester, Tom and Peters, Jannik},
title = {{Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities}},
booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
pages = {41:1--41:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-292-1},
ISSN = {1868-8969},
year = {2023},
volume = {272},
editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18575},
URN = {urn:nbn:de:0030-drops-185759},
doi = {10.4230/LIPIcs.MFCS.2023.41},
annote = {Keywords: hedonic games, core stability, algorithmic game theory, computational social choice}
}
