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Stability for couples in the Stable Matching Problem
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problemthestabilitycouplesstableformatching
Problem
In the Stable Matching Problem, it is stated that there can exist cases where the $m$ list of men can be content with their decisions, yet the list of $f$ cannot when the algorithm is run with men's proposals.
From what I read, an unstable match occurs when $m$ and $f$ prefer each other to their current partners.
I am a little lost in the definition of Stable Matching for this case. I'm going over the slides here.
Is a pair $(m, f)$ stable as long as the men are content even though the female's preferences have not been matched?
From what I read, an unstable match occurs when $m$ and $f$ prefer each other to their current partners.
I am a little lost in the definition of Stable Matching for this case. I'm going over the slides here.
Is a pair $(m, f)$ stable as long as the men are content even though the female's preferences have not been matched?
Solution
Yes, it is stable. It doesn't need to assign the optimal choices for both sides. To break a marriage you need two willing parties, unhappiness of one side in a marriage doesn't make it unstable here.
Context
StackExchange Computer Science Q#223, answer score: 8
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