What is the difference between strongly stable, weakly stable and super stable matching?

Question

I was reading Stable Marriage Problem(SMP, https://en.wikipedia.org/wiki/Stable_marriage_problem) with indifference and I came across the terms strongly stable, weakly stable and super stable matching. What is the difference between them?

Answer 1

In my opinions, they are three stable matching status with different degrees of requirements for matching on preference lists with ties.

Super stable is the most strict among them, and then the strongly stable, weakly stable has the least restriction at last.

Suppose there is a rogue couple (m,w) who don't match with each other in a matching, they will break the properties of the matching when:

• if m strictly prefers (>) w to his current partner and w strictly prefers m to her current partner, the matching is not even a weakly stable matching.
• if m stictly prefers (>) w to his current partner and w considers m no worse than (>=) her current partner, the matching cannot be a strongly stable matching.
• if m considers w no worse than (>=) his current partner and w strictly prefers(>) m to her current partner, the matching also cannot be a strongly stable matching.
• if m considers w no worse than (>=) his current partner and w considers m no worse than (>=) her current partner, the matching will no longer be a super stable matching.