Matching with Incomplete Preferences

Abstract

We study a two-sided marriage market in whic agents have incomplete preferences—i.e., they find some alternatives incomparable. The strong (weak) core consists of matchings wherein no coalition wants to form a new match between themselves, leaving some (all) agents better off without harming anyone. The strong core may be empty, while the weak core can be too large. We propose the concept of "compromise core''—a nonempty set that sits between the weak and the strong cores. Similarly, we define the men-(women-) optimal core and illustrate its benefit in an application to India's engineering college admissions system.

Keywords: Matching, Market Design, Incomplete Preferences