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.
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