Limiting congestion by limiting applications, or making them costly

 Here's a paper that investigates two alternatives to limiting congestion in college admissions: one is to limit applications, and the other is to add a small cost for each additional application. (This is a current topic of discussion in a number of other applications, including matching of new doctors to residencies.)

Application Costs and Congestion in Matching Markets by YingHua He and Thierry Magnac, The Economic Journal,  https://doi.org/10.1093/ej/ueac038 (online early)

Abstract: "A matching market often requires recruiting agents, or ‘programmes’, to costly screen ‘applicants’, and congestion increases with the number of applicants to be screened. We investigate the role of application costs: higher costs reduce congestion by discouraging applicants from applying to certain programmes; however, they may harm match quality. In a multiple-elicitation experiment conducted in a real-life matching market, we implement variants of the Gale-Shapley deferred-acceptance mechanism with different application costs. Our experimental and structural estimates show that a (low) application cost effectively reduces congestion without harming match quality."

"Our empirical strategy is novel. It begins with a multiple-elicitation field experiment that enables us to directly evaluate the effects of application costs. The experiment involves the real-life matching of 129 applicants to the seven master’s programmes at the Toulouse School of Economics (TSE), and was conducted in May 2013 for admission in the 2013–4 academic year. The experimental market designs are three variants of the Gale-Shapley deferred-acceptance (DA) mechanism encountered in practice: the traditional DA mechanism, under which applicants can apply to all programmes without any cost; the DA mechanism with truncation (DA-T), under which applicants can apply to no more than four programmes (hence, DA-T-4); and the DA mechanism with cost (DA-C), under which applicants must write a motivation letter for each additional application beyond the first three applications. Under each mechanism, every applicant is required to submit a rank-ordered list of programmes (ROL). As applicants are informed that one of the mechanisms will be implemented, they have incentives to behave optimally under each mechanism.

"To evaluate the performance of a matching procedure, we focus on two dimensions of a matching outcome: the congestion and match quality. The former is measured by screening costs and approximated by the number of applicants to screen; the latter is measured by the welfare of both sides, the number of unmatched applicants, as well as the number of blocking pairs. A pair comprising applicant and programme blocks a matching if both would be better off by being matched together after leaving their current matches. The stability of a matching, defined as the absence of any blocking pair, is the key to the success of matching markets (Roth, 1991). Importantly, stability implies Pareto efficiency when both sides are endowed with strict preferences (Abdulkadiroğlu and Sönmez, 2013)."