, Andrew Postlewaite and Larry Samuelson “ Matching with Incomplete Information ”

A large literature uses matching models to analyze markets with two-sided heterogeneity, studying problems such as the matching of students to schools, residents to hospitals, husbands to wives, and workers to firms. The analysis typically assumes that the agents have complete information, and examines core outcomes. We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of complete-information stable outcomes. We provide sufficient conditions for incomplete-information stable matchings to be efficient. ∗For helpful comments and suggestions, we thank Yeon-Koo Che, Prajit Dutta, Nicole Immorlica, Fuhito Kojima, Dilip Mookherjee, Andrea Pratt, Bernard Salanie, Roberto Serrano, and Rajiv Vohra. †We thank the National Science Foundation (grants SES-0350969, SES0549946, SES-0648780, and SES-1153893) for financial support. Matching with Incomplete Information by Qingmin Liu, George J. Mailath, Andrew Postlewaite, and Larry Samuelson