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Provide a clear proof / solution to this problem on unique stable matchings Let there be n students and n universities, each with capacity one.
Provide a clear proofsolution to this problem on unique stable matchings
Let there be students and universities, each with capacity one. Recall that a list of prefer
ences, vec:dots,: defines a stable matching instance. Consider an instance vec where every
student has exactly the same strict preference ordering over universities. That is for all students
but you may not make any assumptions on the university preferences.
Prove that, in any instance vec where every student has the same strict preferences, that there is
a unique stable matching for vec That is there is a single matching that is stable for vec and any
other matching is unstable for vec
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