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Boundaries to Single-Agent Stability in Additively Separable Hedonic Games

Author Martin Bullinger

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Author Details

Martin Bullinger
  • Technical University of Munich, Germany

Funding

  • Bullinger, Martin: Deutsche Forschungsgemeinschaft, grants BR 2312/11-2, BR 2312/12-1.

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

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