Speed dating matching algorithm
At the end, there cannot be a man and a woman both unengaged, as he must have proposed to her at some point (since a man will eventually propose to everyone, if necessary) and, being proposed to, she would necessarily be engaged (to someone) thereafter.
Let Alice and Bob both be engaged, but not to each other.
I.e, no man can get a better matching for himself by misrepresenting his preferences.
Moreover, the GS algorithm is even group-strategy proof for men, i.e., no coalition of men can coordinate a misrepresentation of their preferences such that all men in the coalition are strictly better-off.
The GS algorithm is non-truthful for the women (the reviewing side): each woman may be able to misrepresent her preferences and get a better match.
In a uniformly-random instance of the stable marriage problem with n men and n women, the average number of stable matchings is asymptotically In stable matching with indifference, some men might be indifferent between two or more women and vice versa.
If Bob prefers Alice to his current partner, he must have proposed to Alice before he proposed to his current partner.In 2012, The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel was awarded to Lloyd S. Roth "for the theory of stable allocations and the practice of market design." Billions of users access web pages, videos, and other services on the Internet, requiring each user to be matched to one of (potentially) hundreds of thousands of servers around the world that offer that service.A user prefers servers that are proximal enough to provide a faster response time for the requested service, resulting in a (partial) preferential ordering of the servers for each user.The stable roommates problem is similar to the stable marriage problem, but differs in that all participants belong to a single pool (instead of being divided into equal numbers of "men" and "women").The hospitals/residents problem – also known as the college admissions problem – differs from the stable marriage problem in that a hospital can take multiple residents, or a college can take an incoming class of more than one student.
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