Congestion in applications and interviews, by Arnosti, Johari and Kanoria

 Here's a paper modeling the issue that some labor markets may face congestion related to large numbers of applications followed by costly interviews.

Nick Arnosti, Ramesh Johari, Yash Kanoria (2021) Managing Congestion in Matching Markets. Manufacturing & Service Operations Management 23(3):620-636. https://doi.org/10.1287/msom.2020.0927

Abstract. "Problem definition: Participants in matching markets face search and screening costs when seeking a match. We study how platform design can reduce the effort required to find a suitable partner. Practical/academic relevance: The success of matching platforms requires designs that minimize search effort and facilitate efficient market clearing.

"Methodology: We study a game-theoretic model in which “applicants” and “employers” pay costs to search and screen. An important feature of our model is that both sides may waste effort: Some applications are never screened, and employers screen applicants who may have already matched. We prove existence and uniqueness of equilibrium and characterize welfare for participants on both sides of the market. Results: We identify that the market operates in one of two regimes: It is either screening-limited or application-limited. In screening-limited markets, employer welfare is low, and some employers choose not to participate. This occurs when application costs are low and there are enough employers that most applicants match, implying that many screened applicants are unavailable. In application-limited markets, applicants face a “tragedy of the commons” and send many applications that are never read. The resulting inefficiency is worst when there is a shortage of employers. We show that simple interventions—such as limiting the number of applications that an individual can send, making it more costly to apply, or setting an appropriate market-wide wage—can significantly improve the welfare of agents on one or both sides of the market. 

"Managerial implications: Our results suggest that platforms cannot focus exclusively on attracting participants and making it easy to contact potential match partners. A good user experience requires that participants not waste effort considering possibilities that are unlikely to be available. The operational interventions we study alleviate congestion by ensuring that potential match partners are likely to be available.

And from the Conclusion:

"We also compare the effects of an application limit to those of other available levers: either raising application costs or lowering the wage paid to applicants. Although these interventions can lead to thesame aggregate welfare as an application limit, they differ in how they distribute this welfare. Charging fees and lowering wages both increase aggregate welfare at the expense of applicants. Although these interventions may be appropriate for a platform looking to monetize its services or attract more employers, an application limit can yield Pareto improvements in welfare and may be more suitable if the platform is primarily concerned with applicant welfare. These considerations might explain why the tutoring platform TutorZ charges tutors for each potential client that they contact, whereas the dating platforms Coffee Meets Bagel and Tinder limit the number of likes/right swipes permitted in a certain period."