Matching the Marriage Markets
The extent to which the concepts and methodologies we learn in “Networks” are applicable to the world is incredible. I find myself extrapolating things I’ve learned in this class to every part of my life, especially in social situations (for example, how are the strongly connected groups in a house party connected? and how does the strange guy counting everyone in the corner factor in?) Likewise, two men David Gale and Lloyd Shapley, noticed the similarities between the way men propose marriage and the way students apply for college. Many people since then have asked the question, “How does the principle of matching markets apply to marriages?”. This question is obviously very complicated with many subtleties that inhibit a good analysis of a small scale, real world example. Regardless, the idea is very intriguing and has interested scholars for many years. That which follows is a breakdown of the method of matching markets as applied to marriage.
This market is described as discrete-two sided market without money. There are two sets, one set of men one set of women. Men (or a woman) can prefer one woman (man) over another, they can prefer one woman over being single and they can prefer being single over one woman. There is a stable matching when a man prefers a given women to all other available options and that women prefers him to all other options. Using these principles and some other assumptions, one can run an algorithm where each man proposes to his most preferred woman, is accepted or rejected, eventually moving down his line of preferred women until he is matched or single. This algorithm is similar to that of deferred collegiate acceptance
Several curious consequences arise from this setup. one of which is that when men propose the matching is men-optimal, every man weakly prefers men optimal matching to any other matching. When women propose, it creates a women optimal matching. Another extremely interesting consequence of this set-up is that truth telling is an optimal strategy for those who propose.
http://people.duke.edu/~aa88/articles/WorldCongressSurvey.pdf