Matchings with externalities and attitudes

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. Under this framework, we analyze many-to-many matchings and one-to-one matchings where agents take different attitudes when reasoning about the actions of others. In particular, we study optimistic, neutral and pessimistic attitudes and provide both computational hardness results and polynomial-time algorithms for computing stable outcomes.