论文标题
与合同的无数次无数次无数匹配的晶格
The lattice of envy-free many-to-many matchings with contracts
论文作者
论文摘要
我们研究了与合同的多对多匹配模型中的无嫉妒分配，其中市场一侧的代理（医生）赋予了市场另一侧（医院）的替代选择功能，并具有响应良好的偏好。嫉妒的柔软性是稳定性的削弱，允许阻止涉及空缺职位的医院的合同，并且医生不羡慕医院目前雇用的任何医生。我们表明，一组无嫉妒的分配具有晶格结构。此外，我们在此晶格上定义了Tarski操作员，并使用它来对空置链动态过程进行建模，从任何无嫉妒的分配开始，可以达到稳定的分配。
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.
