中文摘要
我们研究带合同的多对多匹配，其中每个参与人可以与同一参与人签订多份合同；换言之，本模型不假设单一性（unitarity）条件。我们提出一个更弱的可替代性条件，称为跨医生可替代性（substitutability across doctors），它是对单边可替代性（unilateral substitutability）的推广。我们证明，若每家医院的选择函数满足跨医生可替代性，且每位医生的选择函数是响应性的（responsive），则稳定结果存在。我们通过推广累积报价过程（cumulative offer process）建立了这一结果。此外，我们提出一个更弱的可替代性条件，该条件纳入了算法运行过程中医生合同报价的可观察性；即使将跨医生可替代性替换为该更弱条件，同一算法仍能保证稳定结果的存在。我们还给出一类满足该更弱条件的具体选择函数，可应用于临时用工市场，尤其是派遣机构可能向每个客户指派多名临时工的情形。
Abstract
We consider many-to-many matching with contracts where each agent can sign multiple contracts with the same agent. In other words, the unitarity condition is not assumed in this model. We offer a weaker substitutability condition called substitutability across doctors, which is a generalization of unilateral substitutability. We show that if every hospital’s choice function satisfies substitutability across doctors and every doctor’s choice function is responsive, then a stable outcome exists. We establish this result by generalizing the cumulative offer process. Moreover, we propose an even weaker substitutability condition that incorporates observability of doctors’ contract offers during the algorithm. The same algorithm guarantees the existence of a stable outcome even when substitutability across doctors is replaced with the weaker condition. We additionally present a specific class of choice functions satisfying the weaker condition that can be applied to a temporary staffing market, particularly in which temp agencies may assign multiple temporary workers to each client.