Matching with Incomplete Preferences

TL;DR

This paper introduces the 'compromise core' concept for two-sided markets with incomplete preferences, providing a nonempty solution set that balances stability and inclusiveness, with applications to college admissions.

Contribution

It proposes the 'compromise core' as a new solution concept for markets with incomplete preferences, bridging the gap between the strong and weak cores.

Findings

The strong core can be empty in markets with incomplete preferences.

The weak core can be excessively large, reducing its usefulness.

The 'compromise core' is nonempty and offers a balanced solution.

Abstract

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.