School choice with vouchers

Official URL: http://dx.doi.org/10.1016/j.jet.2018.10.013

We introduce a novel school-choice with vouchers model. A feasibility notion is defined to incorporate the constraint that students from low-income families need a voucher to go to a private school. We then introduce a stability notion, while emphasizing that the traditional school-choice model and usual stability notion are realized as a special case of our formulation. A class of feasible, stable, and constrained efficient mechanisms is proposed. However, feasibility and stability are incompatible with strategy-proofness in the sense that no mechanism is feasible, stable, and strategy-proof at the same time, implying that any mechanism in our class is manipulable. Given the efficiency and strategic disadvantages of stability, as an alternative solution, we introduce a feasible, efficient, and strategy-proof mechanism. Lastly, we provide a comparative statics analysis.