Does a Stable marriage matching exist when all men have the same preferences for women, but the women do not have the same preferences when it comes to men?
One example case is:
Man 1 pref.: Woman 1, Woman 2
Man 2 pref.: Woman 1, Woman 2
Woman 1 pref.: Man 1, Man 2
Woman 2 pref.: Man 2, Man 1
TIA!
By the stable marriage theorem, there is always a stable marriage no matter what the preferences are.
In your example, a stable marriage would M1-W1 and M2-W2. This is stable because each woman is matched with her most preferred man.