Fractional Hedonic Games

@article{Aziz2014FractionalHG,
  title={Fractional Hedonic Games},
  author={H. Aziz and F. Brandt and Paul Harrenstein},
  journal={ACM Transactions on Economics and Computation (TEAC)},
  year={2014},
  volume={7},
  pages={1 - 29}
}
The work we present in this article initiated the formal study of fractional hedonic games (FHGs), 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. FHGs thus not only constitute a natural class of succinctly representable coalition… Expand
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It is shown that deciding the existence of stable partitions (and therefore also computing stable partitions) is NP-hard for all considered stability notions and that checking whether the valuation functions of a fractional hedonic game induce strict preferences over coalitions is coNP-complete. Expand
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