We study envy-free allocations in a many-to-many matching model with contracts in which agents on one side of the market (doctors) are endowed with substitutable choice functions and agents on the other side of the market (hospitals) are endowed with responsive preferences. Envy-freeness is a weakening of stability that allows blocking contracts involving a hospital with a vacant position and a doctor that does not envy any of the doctors that the hospital currently employs. We show that the set of envy-free allocations has a lattice structure. Furthermore, we define a Tarski operator on this lattice and use it to model a vacancy chain dynamic process by which, starting from any envy-free allocation, a stable one is reached.

我们研究了多对多匹配模型中的无嫉妒分配，其中市场一侧的代理人（医生）被赋予了可替代的选择功能，而市场另一侧的代理人（医院）被赋予了响应偏好。无嫉妒是一种稳定性的削弱，它允许阻止涉及有空缺职位的医院和不嫉妒医院目前雇用的任何医生的医生的合同。我们表明，无嫉妒分配集具有晶格结构。此外，我们在这个格子上定义了一个 Tarski 算子，并用它来模拟一个空位链动态过程，从任何无嫉妒分配开始，达到一个稳定的分配。