Boundaries to Single-Agent Stability in Additively Separable Hedonic Games

Author Martin Bullinger



PDF
Thumbnail PDF

File

LIPIcs.MFCS.2022.26.pdf
  • Filesize: 0.65 MB
  • 15 pages

Document Identifiers

Author Details

Martin Bullinger
  • Technical University of Munich, Germany

Acknowledgements

I would like to thank Felix Brandt and Leo Tappe for the helpful discussions.

Cite AsGet BibTex

Martin Bullinger. Boundaries to Single-Agent Stability in Additively Separable Hedonic Games. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.MFCS.2022.26

Abstract

Coalition formation considers the question of how to partition a set of agents into coalitions with respect to their preferences. Additively separable hedonic games (ASHGs) are a dominant model where cardinal single-agent values are aggregated into preferences by taking sums. Output partitions are typically measured by means of stability, and we follow this approach by considering stability based on single-agent movements (to join other coalitions), where a coalition is defined as stable if there exists no beneficial single-agent deviation. Permissible deviations should always lead to an improvement for the deviator, but they may also be constrained by demanding the consent of agents involved in the deviations, i.e., by agents in the abandoned or welcoming coalition. Most of the existing research focuses on the unanimous consent of one or both of these coalitions, but more recent research relaxes this to majority-based consent. Our contribution is twofold. First, we settle the computational complexity of the existence of contractually Nash stable partitions, where deviations are constrained by the unanimous consent of the abandoned coalition. This resolves the complexity of the last classical stability notion for ASHGs. Second, we identify clear boundaries to the tractability of stable partitions under majority-based stability concepts by proving elaborate hardness results for restricted classes of ASHGs. Slight further restrictions lead to positive results.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Multi-agent systems
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Coalition Formation
  • Hedonic Games
  • Stability

Metrics

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

References

  1. H. Aziz and F. Brandl. Existence of stability in hedonic coalition formation games. In Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 763-770, 2012. Google Scholar
  2. H. Aziz, F. Brandl, F. Brandt, P. Harrenstein, M. Olsen, and D. Peters. Fractional hedonic games. ACM Transactions on Economics and Computation, 7(2):1-29, 2019. Google Scholar
  3. H. Aziz, F. Brandt, and H. G. Seedig. Computing desirable partitions in additively separable hedonic games. Artificial Intelligence, 195:316-334, 2013. Google Scholar
  4. 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
  5. C. Ballester. NP-completeness in hedonic games. Games and Economic Behavior, 49(1):1-30, 2004. Google Scholar
  6. S. Banerjee, H. Konishi, and T. Sönmez. Core in a simple coalition formation game. Social Choice and Welfare, 18:135-153, 2001. Google Scholar
  7. V. Bilò, A. Fanelli, M. Flammini, G. Monaco, and L. Moscardelli. Nash stable outcomes in fractional hedonic games: Existence, efficiency and computation. Journal of Artificial Intelligence Research, 62:315-371, 2018. Google Scholar
  8. A. Bogomolnaia and M. O. Jackson. The stability of hedonic coalition structures. Games and Economic Behavior, 38(2):201-230, 2002. Google Scholar
  9. F. Brandt and M. Bullinger. Finding and recognizing popular coalition structures. Journal of Artificial Intelligence Research, 74:569-626, 2022. Google Scholar
  10. F. Brandt, M. Bullinger, and L. Tappe. Single-agent dynamics in additively separable hedonic games. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI), 2022. Forthcoming. Google Scholar
  11. F. Brandt, M. Bullinger, and A. Wilczynski. Reaching individually stable coalition structures in hedonic games. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 5211-5218, 2021. Google Scholar
  12. M. Bullinger. Pareto-optimality in cardinal hedonic games. In Proceedings of the 19th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 213-221, 2020. Google Scholar
  13. M. Bullinger and S. Kober. Loyalty in cardinal hedonic games. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI), pages 66-72, 2021. Google Scholar
  14. R. Carosi, G. Monaco, and L. Moscardelli. Local core stability in simple symmetric fractional hedonic games. In Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 574-582, 2019. Google Scholar
  15. K. Cechlárová and A. Romero-Medina. Stability in coalition formation games. International Journal of Game Theory, 29:487-494, 2001. Google Scholar
  16. D. Dimitrov, P. Borm, R. Hendrickx, and S. C. Sung. Simple priorities and core stability in hedonic games. Social Choice and Welfare, 26(2):421-433, 2006. Google Scholar
  17. D. Dimitrov and S. C. Sung. On top responsiveness and strict core stability. Journal of Mathematical Economics, 43(2):130-134, 2007. Google Scholar
  18. J. H. Drèze and J. Greenberg. Hedonic coalitions: Optimality and stability. Econometrica, 48(4):987-1003, 1980. Google Scholar
  19. E. Elkind, A. Fanelli, and M. Flammini. Price of pareto optimality in hedonic games. Artificial Intelligence, 288:103357, 2020. Google Scholar
  20. E. Elkind and M. Wooldridge. Hedonic coalition nets. In Proceedings of the 8th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pages 417-424, 2009. Google Scholar
  21. M. Gairing and R. Savani. Computing stable outcomes in symmetric additively separable hedonic games. Mathematics of Operations Research, 44(3):1101-1121, 2019. Google Scholar
  22. D. Gale and L. S. Shapley. College admissions and the stability of marriage. The American Mathematical Monthly, 69(1):9-15, 1962. Google Scholar
  23. M. Hoefer, D. Vaz, and L. Wagner. Dynamics in matching and coalition formation games with structural constraints. Artificial Intelligence, 262:222-247, 2018. Google Scholar
  24. A. B. Kahn. Topological sorting of large networks. Communications of the ACM, 5(11):558-562, 1962. Google Scholar
  25. R. M. Karp. Reducibility among combinatorial problems. In R. E. Miller and J. W. Thatcher, editors, Complexity of Computer Computations, pages 85-103. Plenum Press, 1972. Google Scholar
  26. M. Olsen. On defining and computing communities. In Proceedings of the 18th Computing: Australasian Theory Symposium (CATS), volume 128 of Conferences in Research and Practice in Information Technology (CRPIT), pages 97-102, 2012. Google Scholar
  27. W. Suksompong. Individual and group stability in neutral restrictions of hedonic games. Mathematical Social Sciences, 78:1-5, 2015. Google Scholar
  28. S. C. Sung and D. Dimitrov. On myopic stability concepts for hedonic games. Theory and Decision, 62(1):31-45, 2007. Google Scholar
  29. S. C. Sung and D. Dimitrov. Computational complexity in additive hedonic games. European Journal of Operational Research, 203(3):635-639, 2010. 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