论文标题
在最佳运输中可行的集合映射的连续性
On the Continuity of the Feasible Set Mapping in Optimal Transport
论文作者
论文摘要
考虑两个完整的，可分开的度量空间的乘积上给定边缘分布的概率度量集，当边缘分布变化时，它被视为对应关系。在最佳运输问题中，鉴于Berge的最大定理，这种对应关系的连续性通常需要在边际分布中建立价值函数的连续性，以及一组最佳运输计划的稳定性。 Bergin（1999）建立了这种对应关系的连续性，在本说明中，我们提供了一个新颖的，更短的证据，证明了这一重要结果。然后，我们检查了具有未知类型分布的分配游戏（可转移实用程序匹配问题）的应用程序。
Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity of this correspondence from marginal to joint distributions is often desired, in light of Berge's Maximum Theorem, to establish continuity of the value function in the marginal distributions, as well as stability of the set of optimal transport plans. Bergin (1999) established the continuity of this correspondence, and in this note, we present a novel and considerably shorter proof of this important result. We then examine an application to an assignment game (transferable utility matching problem) with unknown type distributions.
