Matching with Incomplete Preferences

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.