“…Beyond the specific context of reserve system design, our paper relates to the large literature on market design under various classes of distributional constraints such as lower quotas, upper quotas, and regional quotas. A partial list includes Abdulkadiroglu (2005), Biro, Fleiner, Irving, and Manlove (2010), Kojima (2012), Budish, Che, Kojima, and Mil-grom (2013), Westkamp (2013), Ehlers, Hafalir, Yenmez, and Yildirim (2014), Echenique and Yenmez (2015), Kamada and Kojima (2015, Bo (2016), Dogan (2016), Fragiadakis and Troyan (2017), and Abdulkadiroglu and Grigoryan (2021). Our paper is also related to the literature studying the formal properties of allocation processes in the field.…”