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矩阵对策的公平性研究
引用本文:姜殿玉,刘广智.矩阵对策的公平性研究[J].运筹学学报,2003,7(4):12-21.
作者姓名:姜殿玉  刘广智
作者单位:1. 淮海工学院数理科学系,连云港,222005
2. 大连大学信息工程学院,大连,116622
基金项目:National Natural Science Foundation (No.78970025).
摘    要:众所周知,零和二人有限对策也称为矩阵对策。设做一个矩阵对策的两个局中人都希望对策结果尽可能公平。当两个局中人使用对策解中的策略进行对策时,如果对策结果最公平,那么这个对策解称为最优的。本文证明了最优对策解集的一些性质,然后给出矩阵对策公平度的概念并证明了它的一些有趣的性质。

关 键 词:矩阵对策  公平性  对策解  公平度

A Study on Equitablity of a Matrix Game
DIANYU JIANG GUANGZHI LIU Depautment of Mathematics and Physics,Huaihai Institute of Technology,Lianyungang ,China, College of Information Engineering,Dalian University,Dalian ,China.A Study on Equitablity of a Matrix Game[J].OR Transactions,2003,7(4):12-21.
Authors:DIANYU JIANG GUANGZHI LIU Depautment of Mathematics and Physics  Huaihai Institute of Technology  Lianyungang  China  College of Information Engineering  Dalian University  Dalian  China
Institution:DIANYU JIANG GUANGZHI LIU Depautment of Mathematics and Physics,Huaihai Institute of Technology,Lianyungang 222005,China, College of Information Engineering,Dalian University,Dalian 116622,China,
Abstract:It is common knowledge that a zero sum two-person finite game is also called matrix game. Suppose two players who play a matrix game hope that the game result is as equitable as possible. A game solution is called optimal if the game result is most equitable when two players use the strategies in the game solution. In this paper, we prove some properties of a set of optimal game solutions. And we also give the concept of equitable degree of a matrix game and prove some interesting results about it.
Keywords:OR  matrix game  optimal game solution  equitable degree
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