Doctor-Optimal Stability in Unitary Many-to-Many Markets

Abstract

We study bilaterally unitary many-to-many doctor--hospital matching with contracts, taking choice functions as primitives. Doctor choices are substitutable and satisfy irrelevance of rejected contracts, while hospital choices are unilaterally substitutable and satisfy the same condition. Every trajectory of the doctor-proposing cumulative offer process terminates at the greatest stable allocation under the doctor Blair order. We also introduce weakly hospital-quasi-stable allocations and show that they form a finite lattice whose greatest element is stable. Hence, the cumulative-offer outcome, the greatest weakly hospital-quasi-stable allocation, and the doctor-optimal stable allocation coincide. The common allocation is hospital-pessimal in the revealed-choice sense. Under the law of aggregate demand, every agent signs the same number of contracts at all stable allocations.