  In many matching markets, one side "applies" to the other, and these
applications are often expensive and time-consuming (e.g. students applying to
college). It is tempting to think that making the application process easier
should benefit both sides of the market. After all, the applicants could submit
more applications, and the recipients would have more applicants to choose
from. In this paper, we propose and analyze a simple model to understand
settings where both sides of the market suffer from increased number of
applications.
  The main insights of the paper are derived from quantifying the signal to
noise tradeoffs in random matchings, as applications provide a signal of the
applicants' preferences. When applications are costly the signal is stronger,
as the act of making an application itself is meaningful. Therefore more
applications may yield potentially better matches, but fewer applications
create stronger signals for the receiving side to learn true preferences.
  We derive analytic characterizations of the expected quality of stable
matchings in a simple utility model where applicants have an overall quality,
but also synergy with specific possible partners. Our results show how reducing
application cost without introducing an effective signaling mechanism might
lead to inefficiencies for both sides of the market.
