Substitutes for Nonunitary Many-to-Many Matching with Contracts
研究了多对多匹配模型中不要求单一性条件的情况，提出了更弱的替代性条件，并证明在该条件下稳定结果存在，适用于临时用工市场等场景。
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.