标题： Carathéodory型选择与不连续对应关系的随机不动点定理 显示英文标题

标题： Carathéodory-type selection and random fixed point theorems for discontinuous correspondences

摘要： 经济学和博弈论的研究需要关于Carathéodory型选择的结果。 特别是，必须从不需要连续（既不下半连续也不上半连续）的对应关系中获得Carathéodory型选择。 我们提供了关于Carathéodory型选择的新定理，这些定理包括Kim-Prikry-Yannelis\cite{KPY:87}的结果作为推论。 我们还获得了新的随机不动点定理、随机极大元素、随机（Nash）均衡和贝叶斯均衡，扩展并推广了Browder\cite{Browder:68}、Fan\cite{Fan:52}和Nash\cite{Nash}等人的定理，以及其他一些定理。 显示英文摘要

摘要： Research in Economics and Game theory has necessitated results on Carath\'eodory-type selections. In particular, one has to obtain Carath\'eodory type-selections from correspondences that need not be continuous (neither lower-semicontinuous nor upper-semicontinuous). We provide new theorems on Carath\'eodory type-selections that include as corollaries the results in Kim-Prikry-Yannelis \cite{KPY:87}. We also, obtain new random fixed-point theorems, random maximal elements, random (Nash) equilibrium and Bayesian equilibrium extending and generalizing theorems of Browder \cite{Browder:68}, Fan \cite{Fan:52} and Nash \cite{Nash}, among others.