  I study a two-sided marriage market in which 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. I
propose the concept of the "compromise core" -- a nonempty set that sits
between the weak and the strong cores. Similarly, I define the men-(women-)
optimal core and illustrate its benefit in an application to India's
engineering college admissions system.
