Strategyproof matching with minimum quotas

We study matching markets in which institutions may have minimum and maximum quotas. Minimum quotas are important in many settings, such as hospital residency matching, military cadet matching, and school choice, but current mechanisms are unable to accommodate them, leading to the use of ad hoc solutions. We introduce two new classes of strategyproof mechanisms that allow for minimum quotas as an explicit input and show that our mechanisms improve welfare relative to existing approaches. Because minimum quotas cause a theoretical incompatibility between standard fairness and nonwastefulness properties, we introduce new second-best axioms and show that they are satisfied by our mechanisms. Last, we use simulations to quantify (1) the magnitude of the potential efficiency gains from our mechanisms and (2) how far the resulting assignments are from the first-best definitions of fairness and nonwastefulness. Combining both the theoretical and simulation results, we argue that our mechanisms will improve the performance of matching markets with minimum quota constraints in practice.