The [[weighted matching problem]] is to find a matching in a weighted [[bipartite graph]] that has maximum weight. Maximum weighted matchings do not have to be stable, but in some applications a maximum weighted matching is better than a stable one.
==Observations==
The SMP can be used to illustrate certain social phenomena, such as the effect of [[beauty]] on partner choice. When the preferences of the men and women are purely random, everyone is quite likely to get a partner that is high on their preference list. However, if the preferences tend to aim at certain beautiful individuals, a person's chances of getting a partner they really want is drastically reduced, as their top choices are massively in demand. Hence, it has been said that the SMP proves that beauty just makes everyone unhappy.
