My new paper, "Exit Option Can Make Cooperation Easier" (joint with Takako Fujiwara-Greve) is uploaded at SSRN. The manuscript is very short (only 7 pages!). Please take a look if you are interested in how introducing exit option would affect cooperative incentives.
A completely different paper on matching, "Expanding "Choice" in School Choice" (joint with Atila Abdulkadiroğlu, Yeon-Koo Che) was finally published in the American Economic Journal: Microeconomics. (as a lead article!) Our earlier paper, "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered", appeared in the American Economic Review, was originally a part of this AEJ paper. Both are theoretical works but contains important policy implications on public school choice. It would be very nice if you could read (and hopefully cite) the articles :)