Before revision:  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:  In our formalization, students have consistent (lexicographic) preferences over advisors and co-advisors (consistent preferences), while advisors and co-advisors have preferences over students only (hence advisors and co-advisors are cooperative).