Mathematical strategame theory

Abstract

The stable matching problem is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences of each element. In 1962, David Gale and Lloyd Shapley proved that, for any equal number of men and women, it is always possible to solve the Stable matching problem and make all marriages stable. It’s famous Gale-Shapley Algorithm. It also successfully applied on the National Residency Matching Program, has improved the stable matching rate between medical students and hospitals. It also extends to the more complex similar problems: Stable roommate problem, Hospitals/residents problem and hospitals/residents problem with couples. Some of them may not have stable matching solutions in the extreme conditions in the real world. However the more extensions and modification will be made to the basic stable matching algorithm, the more algorithms will be applicable for real world instances