  In hedonic diversity games (HDGs), recently introduced by Bredereck, Elkind
and Igarashi (2019), each agent belongs to one of two classes (men and women,
vegetarians and meat-eaters, junior and senior researchers), and agents'
preferences over coalitions are determined by the fraction of agents from their
class in each coalition. Bredereck et al. show that while an HDG may fail to
have a Nash stable (NS) or a core stable (CS) outcome, every HDG in which all
agents have single-peaked preferences admits an individually stable (IS)
outcome, which can be computed in polynomial time. In this work, we extend and
strengthen these results in several ways. First, we establish that the problem
of deciding if an HDG has an NS outcome is NP-complete, but admits an XP
algorithm with respect to the size of the smaller class. Second, we show that,
in fact, all HDGs admit IS outcomes that can be computed in polynomial time;
our algorithm for finding such outcomes is considerably simpler than that of
Bredereck et al. We also consider two ways of generalizing the model of
Bredereck et al. to k > 2 classes. We complement our theoretical results by
empirical analysis, comparing the IS outcomes found by our algorithm, the
algorithm of Bredereck et al. and a natural better-response dynamics.
