On the Equivalence of the G-Weak and -Strong Core in the Marriage Problems

In the marriage problems (two-sided one-to-one matching problems), it is well-known that the weak core, the strong core and the set of stable matchings are all equivalent. This paper generalizes the above observation considering the G-weak core and the G-strong core. These are the core concepts in which blocking power is restricted to the coalitions belonging to the prescribed class of coalitions G. I give a necessary and sufficient condition for G to satisfy for the equivalence of the G-weak core and the G-strong core