According to Alvin Roth, a matching market is one where "you don't simply choose what you want, you have to also be chosen". With this in mind, I would like to pose the question about whether the concept of division of labor (in the sense of Ricardo's theory of comparative advantage) applies at all in matching markets? If so, what are the qualifications? Examples would be appreciated. (So far, I haven't been able to find any resources on the web that deal with these two concepts tied together).
P.S- I am interested more in labor and employment related matching markets. There are some papers on division of labor in the marriage market, but I'm not quite interested in that.