00:01
Hello students, welcome back.
00:01
So here, the de -referred acceptance algorithm proposed by the gail and shapley has had a profound influence on the market design both practically and theoretically.
00:11
Matching is one of the most important function of the market.
00:15
Okay, matching is one of the most important function of market.
00:20
Now using a deferred acceptance algorithm makes it safe for the proposing side to make offers according to the opposite person preferences.
00:29
Now, algorithms for finding solutions to the stable marriage problem have applications in a variety of real world situation.
00:37
Now, in mathematics, economics and computer science, the stable marriage problem, also a stable matching problem or smp, is the problem of finding a stable matching between two equally sized sets of elements given or during of preferences for each elements.
00:55
Okay, so these are two sets and we have to consider.
00:59
Preferences of both of them okay so here when all the men and women have strict preferences there always exist an m optimal stable matching that every man likes at least as well as another stable matching and w woman optimal stable matching so the w optimal stable matching is the matching which is produced by the algorithm where the woman proposed so g s proved theorem 2 by showing that in the course of d word acceptance no man is ever rejected by a woman who could be matched to him at a stable matching.
01:36
Okay, so stable matching is very crucial for the theory.
01:41
Now, preferences are strict...