Hedonic diversity games

We consider a coalition formation setting where each agent belongs to one of the two types, and agents' preferences over coalitions are determined by the fraction of the agents of their own type in each coalition. This setting differs from the well-studied Schelling's model in that some agents may prefer homogeneous coalitions, while others may prefer to be members of a diverse group, or a group that mostly consists of agents of the other type. We model this setting as a hedonic game and investigate the existence of stable outcomes using hedonic games solution concepts. We show that a core stable outcome may fail to exist and checking the existence of core stable outcomes is computationally hard. On the other hand, we propose an efficient algorithm to find an individually stable outcome under the natural assumption that agents' preferences over fractions of the agents of their own type are single-peaked