  We study the outcome of deferred acceptance when prospective medical
residents can only apply to a limited set of hospitals. This limitation
requires residents to make a strategic choice about the quality of hospitals
they apply to. Through a mix of theoretical and experimental results, we study
the effect of this strategic choice on the preferences submitted by
participants, as well as on the overall welfare. We find that residents'
choices in our model mimic the behavior observed in real systems where
individuals apply to a mix of positions consisting mostly of places where they
are reasonably likely to get accepted, as well as a few "reach" applications to
hospitals of very high quality, and a few "safe" applications to hospitals of
lower than their expected level. Surprisingly, the number of such "safe"
applications is not monotone in the number of allowed applications. We also
find that selfish behavior can hurt social welfare, but the deterioration of
overall welfare is very minimal.
