  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.
