Speed dating matching algorithm
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.
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.
But this is impossible since such "cycle of rejections" cannot start anywhere: suppose by contradiction that it starts at e.g. The GS algorithm is a truthful mechanism from the point of view of men (the proposing side).
In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element.
A matching is a mapping from the elements of one set to the elements of the other set.
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.