Coalition Formation with Bounded Coalition Size

Chaya Levinger, Sofia Simola, Noam Hazon, Amos Azaria

Research output: Contribution to journalConference articlepeer-review


In many situations when people are assigned to coalitions, the utility of each person depends on the friends in her coalition. Additionally, in many situations, the size of each coalition should be bounded. This paper studies such coalition formation scenarios in both weighted and unweighted settings. Since finding a partition that maximizes the utilitarian social welfare is computationally hard, we provide a polynomial-time approximation algorithm. We also investigate the existence and the complexity of finding stable partitions. Namely, we show that the Contractual Strict Core (CSC) is never empty, but the Strict Core (SC) of some games is empty. Finding partitions that are in the CSC is computationally easy, but even deciding whether an SC of a given game exists is NP-hard. The analysis of the core is more involved. In the unweighted setting, we show that when the coalition size is bounded by 3 the core is never empty, and we present a polynomial time algorithm for finding a member of the core. However, for the weighted setting, the core may be empty, and we prove that deciding whether there exists a core is NP-hard.

Original languageEnglish
Pages (from-to)1119-1127
Number of pages9
JournalProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
StatePublished - 2024
Event23rd International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2024 - Auckland, New Zealand
Duration: 6 May 202410 May 2024


  • Additively separable hedonic games
  • Coalition formation
  • Stability


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