Document Open Access Logo

Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities

Authors Tom Demeulemeester , Jannik Peters

PDF

File

Thumbnail PDF
PDF
LIPIcs.MFCS.2023.41.pdf
  • Filesize: 0.77 MB
  • 14 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Computing methodologies → Multi-agent systems
  • Theory of computation → Algorithmic game theory
Keywords
  • hedonic games
  • core stability
  • algorithmic game theory
  • computational social choice

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

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.

Cite As Get BibTex

Tom Demeulemeester and Jannik Peters. Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.MFCS.2023.41

Author Details

Tom Demeulemeester
  • KU Leuven, Belgium
Jannik Peters
  • TU Berlin, Germany

Funding

  • Demeulemeester, Tom: Research Foundation - Flanders (FWO) under the PhD fellowship 11J8721N.
  • Peters, Jannik: Deutsche Forschungsgemeinschaft (DFG) under the grant BR 4744/2-1 and the Graduiertenkolleg "Facets of Complexity" (GRK 2434).

Supplementary Materials

References

  1. H. Aziz and R. Savani. Hedonic games. In F. Brandt, V. Conitzer, U. Endriss, J. Lang, and A. D. Procaccia, editors, Handbook of Computational Social Choice, chapter 15. Cambridge University Press, 2016. Google Scholar
  2. Haris Aziz, Florian Brandl, Felix Brandt, Paul Harrenstein, Martin Olsen, and Dominik Peters. Fractional hedonic games. ACM Transactions on Economics and Computation (TEAC), 7(2):1-29, 2019. Google Scholar
  3. Haris Aziz, Felix Brandt, and Hans Georg Seedig. Computing desirable partitions in additively separable hedonic games. Artificial Intelligence, 195:316-334, 2013. Google Scholar
  4. Haris Aziz, Serge Gaspers, Joachim Gudmundsson, Julián Mestre, and Hanjo Taubig. Welfare maximization in fractional hedonic games. In Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI, pages 461-467, 2015. Google Scholar
  5. Vittorio Bilò, Angelo Fanelli, Michele Flammini, Gianpiero Monaco, and Luca Moscardelli. Nash stable outcomes in fractional hedonic games: Existence, efficiency and computation. Journal of Artificial Intelligence Research, 62:315-371, 2018. Google Scholar
  6. Vittorio Bilò, Gianpiero Monaco, and Luca Moscardelli. Hedonic games with fixed-size coalitions. In Proceedings of the AAAI Conference on Artificial Intelligence, pages 9287-9295, 2022. Google Scholar
  7. Niclas Boehmer, Martin Bullinger, and Anna Maria Kerkmann. Causes of stability in dynamic coalition formation. In Proceedings of the AAAI Conference on Artificial Intelligence, 2023. Forthcoming. Google Scholar
  8. Niclas Boehmer and Edith Elkind. Individual-based stability in hedonic diversity games. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 34(2), pages 1822-1829, 2020. Google Scholar
  9. A. Bogomolnaia and M. O. Jackson. The stability of hedonic coalition structures. Games and Economic Behavior, 38(2):201-230, 2002. Google Scholar
  10. Felix Brandt and Martin Bullinger. Finding and recognizing popular coalition structures. Journal of Artificial Intelligence Research, 74:569-626, 2022. Google Scholar
  11. Felix Brandt, Martin Bullinger, and Leo Tappe. Single-agent dynamics in additively separable hedonic games. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 36(5), pages 4867-4874, June 2022. URL: https://doi.org/10.1609/aaai.v36i5.20415.
  12. Felix Brandt, Martin Bullinger, and Anaëlle Wilczynski. Reaching individually stable coalition structures in hedonic games. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35(6), pages 5211-5218, 2021. Google Scholar
  13. Robert Bredereck, Edith Elkind, and Ayumi Igarashi. Hedonic diversity games. In Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, pages 565-573, 2019. Google Scholar
  14. Martin Bullinger and Stefan Kober. Loyalty in cardinal hedonic games. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI, pages 66-72, 2021. Google Scholar
  15. Raffaello Carosi, Gianpiero Monaco, and Luca Moscardelli. Local core stability in simple symmetric fractional hedonic games. In Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems, pages 574-582, 2019. Google Scholar
  16. Jiehua Chen, Gergely Csáj, Sanjukta Roy, and Sofia Simola. Cores in friend-oriented hedonic games: Verification is surprisingly harder than searching. In Proceedings of the 22nd International Conference on Autonomous Agents and MultiAgent Systems, 2023. Forthcoming. Google Scholar
  17. Jiehua Chen and Sanjukta Roy. Multi-dimensional stable roommates in 2-dimensional euclidean space. In 30th Annual European Symposium on Algorithms, ESA 2022, 2022. Google Scholar
  18. Agnes Cseh, Tamás Fleiner, and Petra Harján. Pareto optimal coalitions of fixed size. Journal of Mechanism and Institution Design, 4:1, 2019. Google Scholar
  19. J. H. Drèze and J. Greenberg. Hedonic coalitions: Optimality and stability. Econometrica, 48(4):987-1003, 1980. Google Scholar
  20. Angelo Fanelli, Gianpiero Monaco, and Luca Moscardelli. Relaxed core stability in fractional hedonic games. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI, pages 182-188, 2021. Google Scholar
  21. Robert Ganian, Thekla Hamm, Dusan Knop, Simon Schierreich, and Ondrej Suchý. Hedonic diversity games: A complexity picture with more than two colors. In Thirty-Sixth AAAI Conference on Artificial Intelligence, AAAI 2022, pages 5034-5042, 2022. Google Scholar
  22. Tesshu Hanaka and Michael Lampis. Hedonic games and treewidth revisited. In 30th Annual European Symposium on Algorithms (ESA 2022), 2022. Google Scholar
  23. Anna Maria Kerkmann, Nhan-Tam Nguyen, Anja Rey, Lisa Rey, Jörg Rothe, Lena Schend, and Alessandra Wiechers. Altruistic hedonic games. Journal of Artificial Intelligence Research, 75:129-169, 2022. Google Scholar
  24. Lily Li, Evi Micha, Aleksandar Nikolov, and Nisarg Shah. Partitioning friends fairly. In Proceedings of the AAAI Conference on Artificial Intelligence, 2023. Forthcoming. Google Scholar
  25. Michael McKay and David Manlove. The three-dimensional stable roommates problem with additively separable preferences. In Algorithmic Game Theory: 14th International Symposium, SAGT 2021, Proceedings, pages 266-280. Springer, 2021. Google Scholar
  26. Gianpiero Monaco, Luca Moscardelli, and Yllka Velaj. Stable outcomes in modified fractional hedonic games. Autonomous Agents and Multi-Agent Systems, 34(1):1-29, 2020. Google Scholar
  27. Martin Olsen. On defining and computing communities. In Proceedings of the Eighteenth Computing: The Australasian Theory Symposium-Volume 128, pages 97-102, 2012. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact