After seeing the marriage, the college and roommate problems I find another application of matching theory in the paper of Kelso and Crawford (1982). I saw this one the last semester in Bertan’s class so for the people who couldn’t take classes with him, here is another problem about matching theory. I also recommend that you read the paper.
Following the salary adjustment process developed by Kelso and Crawford in “Job Matching, Coalition Formation, and Gross Substitutes” (based on Crawford and Knoer algorithm)
Try to solve this problem:
Is the core empty?