# Fractional Hedonic Games

arXiv: https://arxiv.org/abs/1705.10116 · HTML: https://mlsanity.com/paper/1705.10116/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2017.

## Built on by (most cited first, 10 of 10)

- [Proportional Fairness in Non-Centroid Clustering](https://mlsanity.com/paper/2410.23273/) (2024)
- [ULTRA: A Data-driven Approach for Recommending Team Formation in Response to Proposal Calls](https://mlsanity.com/paper/2201.05646/) (2022)
- [Promoting Research Collaboration with Open Data Driven Team Recommendation in Response to Call for Proposals](https://mlsanity.com/paper/2309.09404/) (2023)
- [Coalition Formation in LLM Agent Networks: Stability Analysis and Convergence Guarantees](https://mlsanity.com/paper/2604.14386/) (2026)
- [Maximizing Utilitarian and Egalitarian Welfare of Fractional Hedonic Games on Tree-like Graphs](https://mlsanity.com/paper/2310.05139/) (2023)
- [GRAPE-S: Near Real-Time Coalition Formation for Multiple Service Collectives](https://mlsanity.com/paper/2310.12480/) (2023)
- [Exact Algorithms and Lower Bounds for Forming Coalitions of Constrained Maximum Size](https://mlsanity.com/paper/2505.22384/) (2025)
- [varepsilon-fractional Core Stability in Hedonic Games](https://mlsanity.com/paper/2311.11101/) (2023)
- [The Bakers and Millers Game with Restricted Locations](https://mlsanity.com/paper/2501.05334/) (2025)
- [Metric Hedonic Games on the Line](https://mlsanity.com/paper/2602.05888/) (2026)

## Abstract (arXiv)

The work we present in this paper initiated the formal study of fractional hedonic games, coalition formation games in which the utility of a player is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which players only distinguish between friends and non-friends and desire to be in a coalition in which the fraction of friends is maximal. Fractional hedonic games thus not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of fractional hedonic games is non-empty and provide algorithms for computing a core stable outcome. By contrast, we show that the core may be empty in other cases, and that it is computationally hard in general to decide non-emptiness of the core.