Before revision: We introduce a variant of the three-sided stable matching problem for a PhD market with students, advisors, and co-advisors . In our formalization, students have consistent (lexicographic) preferences over advisors and co-advisors , and the latter have preferences over students only (hence advisors and co-advisors are cooperative).
After revision: We introduce a variant of the three-sided stable matching problem for a PhD market with students, advisors, and co-advisors , and can be generalized to supply chain networks viewed as n-sided markets. In the three-sided PhD market, students primarily care about advisors and then about co-advisors , and the latter have preferences over students only (hence advisors and co-advisors are cooperative).