Floor constraints are a prominent feature of many matching markets, such as medical residency, teacher assignment, and military cadet matching. We develop a theory of matching markets under floor constraints. We introduce a stability notion, which we call floor respecting stability, for markets...

A principal distributes an indivisible good to budget‐constrained agents when both valuation and budget are agents' private information. The principal can verify an agent's budget at a cost. The welfare‐maximizing mechanism can be implemented via a two‐stage scheme. First, agents report...