Slot-specific Priorities with Capacity Transfers

We study two-sided matching markets in which agents match to institutions that may have multiple slots available to accept contracts. In many real-world institutions, there are restrictions for some slots (if not all) either on slot priorities or on the transferability of unfilled slots over others (or both). We construct a rich family of practical choice rules, slot-specific priorities with capacity transfers (SSPwCT), that utilize both independent slot priorities and transferability of vacant slots. We show that the cumulative offer mechanism (COM) is stable, strategy-proof and respects improvements with regards to SSPwCT choice rules. Transferring the capacity of one more unfilled slot, while all else is constant, leads to strategy-proof Pareto improvement of the COM. We also provide comparative static results for expansion of branch capacity and addition of new contracts. Our results have implications for resource allocation problems with diversity considerations.