Umut Dur (North Carolina State University) and myself have a new WP titled “Capacity design in school choice”. The latest version is available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3898719.
Abstract: “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 heuristics solutions to this capacity design problem can be inefficient, even if they focus on allocating seats to the most demanded schools. However, we introduce a simple myopic algorithm that characterizes the set of efficient matchings among those that respect priorities.”