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Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities

Authors Tom Demeulemeester , Jannik Peters

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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).

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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

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.

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

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Supplementary Materials

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