Capacity design in school choice

We study a new variant of the school choice problem in which capacities can be altered by distributing additional seats across schools in response to students' reported preferences. We show that heuristic solutions to this capacity design problem can be inefficient, even if they focus on allocating seats to the most demanded schools. We introduce a simple class of algorithms that, in the problem where additional seats can be distributed, characterizes the set of efficient matchings among those that respect priorities. We also investigate the incentive properties of this class of efficient algorithms.