🤖 AI Summary
This study addresses the implementation of the doctor-optimal stable allocation in many-to-many matching markets between doctors and hospitals. By introducing the notion of weakly hospital-quasi-stable allocations, the authors demonstrate that this set forms a finite lattice whose greatest element coincides precisely with the doctor-optimal stable allocation—also the worst outcome for hospitals among all stable allocations. Leveraging choice functions and a cumulative offer mechanism, and invoking standard matching-theoretic conditions such as substitutability and irrelevance of rejected contracts, the paper establishes that under the law of aggregate demand, the proposed procedure converges to the doctor-optimal stable allocation. Furthermore, it guarantees that all stable allocations yield identical numbers of contracts for each participant.
📝 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.