A dynamic school choice model

This paper inspires from a real-life assignment problem faced by the Mexican Ministry of Public Education. We introduce a dynamic school choice problem that consists in assigning positions to overlapping generations of teachers. From one period to another, teachers can either retain their current positions or choose a preferred one. In this framework, a solution concept that conciliates the fairness criteria with the individual rationality condition is introduced. It is then proved that a solution always exists and that it can be reached by a modified version of the deferred acceptance algorithm of Gale and Shapley. We also show that the mechanism is dynamically strategy-proof, and respects improvements whenever the set of orders is lexicographic by tenure.