Priority Uncertainty and Cutoff Signals in Decentralized College Admissions

Priority structures are uncertain in real-life college admissions markets. This study investigates how information structures on priority affect resulting allocations. To do this, we focus on a class of real-life information structures that are represented as cutoff signals, which privately tell whether a priority exceeds a cutoff, in a simple decentralized college admissions market. The main result characterizes equilibrium distributions under cutoff signals along with simple equilibrium strategies, showing that the cutoff signals implement all implementable state-independent distributions of students across schools. In addition, we find that the cutoff signals have rich properties: All allocations implementable by cutoff signals and straightforward strategies are ex-ante fair. Moreover, these allocations are implementable as unique equilibrium outcomes. The applications include both multiple-sender persuasion and information design. The results indicate that equilibrium allocations are sensitive to priority uncertainty and could be undesirable without appropriate policy intervention. We also characterize implementable outcomes in celebrated centralized admissions systems