Reserve Matching with Thresholds

We develop a general framework for reserve systems that allocate scarce resources such as vaccines to unit-demand agents under prioritization and eligibility constraints, along with a computationally efficient mechanism. Reserve systems allocate scarce resources --such as vaccines, medical units, school seats, or government positions-- to essential groups by creating categories with prioritized beneficiaries. Prior work typically assumed a common baseline priority ordering and featured either hard or soft reserves. The threshold reserve model we introduce supports independent priority orderings, mixtures of hard and soft reserves, and overlapping categories, thereby capturing both beneficiary designations and eligibility constraints while offering policymakers greater flexibility. Our Iterative Max-in-Max Assignment Mechanism (IMMAM) satisfies all desirable properties in this domain: it respects priorities within categories, maximizes resource utilization, and then lexicographically maximizes beneficiary assignments. IMMAM is path independent and therefore well-behaved in settings with multiple institutions making simultaneous allocation decisions. We leverage path independence to obtain comparative statics and to significantly improve the mechanism's computational efficiency. We outline applications of our framework in the context of vaccine allocation.