Effect of selfish choices in deferred acceptance with short lists

TL;DR

This paper examines how limited application options influence medical residents' strategic choices in deferred acceptance algorithms, revealing effects on preferences and welfare with minimal overall impact.

Contribution

It combines theoretical and experimental analysis to understand strategic application behavior and its impact on welfare in constrained matching markets.

Findings

Residents' choices mimic real-world application patterns.

Number of 'safe' applications is non-monotonic with application limits.

Selfish behavior slightly reduces social welfare.

Abstract

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.