简单网络流对策的相对N-核  

Relative Nucleolus of Flow Game on Simple Network

作　　者：方奇志[1] 闫林成[1] 李晖[1] 

机构地区：[1]中国海洋大学数学科学学院,河北青岛266071

出　　处：《数学的实践与认识》2011年第6期125-132,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10771200)

摘　　要：主要研究简单网络流对策中相对N-核的算法.当网络中最大流值等于1时,证明相对N-核与对策的核心相同,不一定是单点集;而当网络中最大流值大于1时,利用Kopelowitz's序列线性规划方法和线性规划对偶理论,证明相对N-核与N-核相同(同为单点集),并且可在局中人个数的多项式时间内得到求解.This paper focuses on the relative nucleolus of the flow game defined on a simple network. When the value of the maximum flow in the network is 1, the relative nucleolus coincides with the core. On the other hand, when the value of the maximum flow in the network is greater than 1, the relative nucleolus coincides with the original nucleolus. The main techniques in our proofs are Kopelowitz＇s sequential linear programming method and linear programming duality theorem. These results yield that the relative nucleolus of a simple flow game can be computed in polynomial time.

关 键 词：网络流 线性规划 对偶 核心 N-核 

分 类 号：O157.5[理学—数学]