Signal to noise in matching markets

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.