Coalitional Affinity Games and the Stability Gap

We present and analyze coalitional affinity games, a family of hedonic games that explicitly model the value that an agent receives from being associated with other agents. We provide a characterization of the social-welfare maximizing coalition structures, and study the stability properties of affinity games, using the core solution concept. Interestingly, we observe that members of the core do not necessarily maximize social welfare. We introduce a new measure, the stability-gap to capture this difference. Using the stability gap, we show that for an interesting class of coalitional affinity games, the difference between the social welfare of a stable coalition structure and a social welfare maximizing coalition structure is bounded by a factor of two, and that this bound is tight.

Simina Branzei, Kate Larson