Peer Effects and Stability in Matching Markets

Many-to-one matching markets exist in numerous different forms, such as college admissions, matching medical interns to hospitals for residencies, assigning housing to college students, and the classic firms and workers market. In all these markets, externalities such as complementarities and peer effects severely complicate the preference ordering of each agent. Further, research has shown that externalities lead to serious problems for market stability and for developing efficient algorithms to find stable matchings. In this paper we make the observation that peer effects are often the result of underlying social connections, and we explore a formulation of the many-to-one matching market where peer effects are derived from an underlying social network. The key feature of our model is that it captures peer effects and complementarities using utility functions, rather than traditional preference ordering. With this model and considering a weaker notion of stability, namely two-sided exchange stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. We also give distributed algorithms that are guaranteed to converge to a two-sided exchange stable matching. To assess the competitive ratio of these algorithms and to more generally characterize the efficiency of matching markets with externalities, we provide general bounds on how far the welfare of the worst-case stable matching can be from the welfare of the optimal matching, and find that the structure of the social network (e.g. how well clustered the network is) plays a large role.

💡 Research Summary

This paper studies many‑to‑one matching markets—illustrated by the problem of assigning undergraduate students to residential houses—under the realistic assumption that agents experience externalities in the form of peer effects and complementarities. Rather than relying on traditional ordinal preference lists, the authors model each agent’s satisfaction with a utility function that explicitly depends on a weighted, undirected social network among the students and on the composition of the groups assigned to each house.

Model.

• Agents: A set of houses (H) each with a quota (q_h) and a set of students (S).
• Network: An undirected weighted graph (G=(V,E,w)) with (V=S); the weight (w(s,t)\ge 0) measures the strength of the friendship between students (s) and (t).
• Utilities:
  • For a student (s) matched to house (\mu(s)), utility is
    \