A Survey of the Stable Marriage Problem and Its Variants

The stable marriage problem is to find a matching between men and women, considering preference lists in which each person expresses his/her preference over the members of the opposite gender. The output matching must be stable, which intuitively means that there is no man- woman pair both of which have incentive to elope. This problem was introduced in 1962 in the seminal paper of Gale and Shapley, and has attracted researchers in several areas, including mathematics, economics, game theory, computer science, etc. This paper introduces old and recent results on the stable marriage problem and some other related problems.