"After a market has been designed, adopted, and implemented, it has a continuing life of its own. For those involved directly in the market, it is useful to continue to monitor it to make sure it is functioning well. For those of us involved in market design, it is also good to check how things are going, as a way to find out if there are unanticipated problems that still need to be addressed. Finally, the design and operation of new marketplaces also raises new theoretical questions, which sometimes lead to progress in economic theory. In this update, I’ll briefly point to developments of each of these kinds, since the publication of Roth (2008), What have we learned from market design?. I’ll discuss theoretical results only informally, to avoid having to introduce the full apparatus of notation and technical assumptions."There is nobody better to ask, and answer, such a question than Roth as he is one of the leaders in the field.
The 2008 paper referred to is available from: Roth, Alvin E. "What have we learned from market design?" Hahn Lecture, Economic Journal, 118 (March), 2008, 285-310.