Matching, cardinal utility, and social welfare

Abstract

Matching markets have historically been an important topic in economics research. On the positive (descriptive) side, researchers have modeled everything ranging from marriage markets to labor markets using the framework of matching. Matching was also one of the first areas in which market design made a name for itself, perhaps most famously in the redesign of the market that matches graduating M.D.s to their first residency programs in the United States. The arrival of computer scientists to the field of market design in general can be traced to many of the reasons suggested recently by Conitzer [2010] (in a broader context than just market design) in an article in Communications of the ACM , including the effects of new markets that have been made possible by advances in networking and Internet technology, a more computational mindset in general, and also the ability to view problems from a different perspective. In the case of matching markets in particular, in addition to the (often) constructive nature of computational approaches, there is also the historical fact that computer scientists have studied matching from many different perspectives, perhaps because matching markets have a very natural representation in the language of graphs.