Sequential School Choice with Public and Private Schools

Motivated by school admission systems used in, e.g., Turkey and Sweden, this paper investigates a sequential two-stage admission system with public and private schools. To perform the analysis, relevant axioms and equilibrium notions need to be tailored for the considered dynamic setting. In particular, a notion of truthfulness, referred to as straightforwardness, is introduced. In sharp contrast to classic one-stage admission systems, sequentiality leads to a trade-off between the existence of a straightforward (i.e., truthful) equilibrium and non-wastefulness. Given this insight, we identify the unique set of rules for two-stage admission systems that guarantees the existence of a straightforward equilibrium and, at the same time, reduces the number of wasted school seats. Several existing admission systems are also theoretically analyzed within our general framework and empirically evaluated using school choice data from Sweden. The latter analysis allows us to quantify various trade-offs in sequential admission systems.