NP-complete stable matching problems
Journal of Algorithms
Stable matchings, optimal assignments, and linear programming
Mathematics of Operations Research
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the complexity of exchange-stable roommates
Discrete Applied Mathematics
On clusterings: Good, bad and spectral
Journal of the ACM (JACM)
Proceedings of The 8th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
Social and Economic Networks
Anarchy, Stability, and Utopia: Creating Better Matchings
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
The exchange-stable marriage problem
Discrete Applied Mathematics
Matching models for preference-sensitive group purchasing
Proceedings of the 13th ACM Conference on Electronic Commerce
Matchings with externalities and attitudes
Proceedings of the 2013 international conference on Autonomous agents and multi-agent systems
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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 twosided exchange stability, we prove that stable matchings always exist and characterize the set of stable matchings in terms of social welfare. To 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.