Application fee manipulations in matching markets

In some well-known hospital–intern type of matching markets, hospitals impose mandatory application fees on internship applicants to consider their applications. Motivated by this real-life phenomenon, we study the application fee overreporting incentives of hospitals in centralized matching markets by assuming that interns have finite budgets to spend on such fees. Our main theorem shows that no stable mechanism is immune to application fee manipulations. Interestingly, under any stable rule, hospitals might not only obtain better matchings but also increase their application fee revenues through overreporting their application fees. In the restricted domains in which either side has homogeneous preferences or each hospital has only one available position, every stable mechanism turns out to be immune to application fee overreportings.