  Two-sided matchings are an important theoretical tool used to model markets
and social interactions. In many real life problems the utility of an agent is
influenced not only by their own choices, but also by the choices that other
agents make. Such an influence is called an externality. Whereas fully
expressive representations of externalities in matchings require exponential
space, in this paper we propose a compact model of externalities, in which the
influence of a match on each agent is computed additively. In this framework,
we analyze many-to-many and one-to-one matchings under neutral, optimistic, and
pessimistic behaviour, and provide both computational hardness results and
polynomial-time algorithms for computing stable outcomes.
