两类2人非合作有限博弈分类的可行性  

Feasibility of classification on two kinds of 2-person noncooperative finite games

作　　者：胡明[1] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003

出　　处：《江苏科技大学学报（自然科学版）》2010年第4期405-409,共5页Journal of Jiangsu University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(40904034)

摘　　要：从2人非合作有限博弈的数学结构出发,通过Baire纲和测度两种方法,证明了在这两种意义下,对绝大多数2人非合作有限博弈分类的可行性.首先,证明了在Baire纲意义下,当一个局中人的策略选定,另一个局中人的最优策略唯一时对应的2人有限非合作博弈在所有2人有限博弈中占绝大多数;其次,证明了在测度意义下,当一个局中人的策略选定,另一个局中人有多个最优策略时对应的2人有限非合作博弈在所有2人有限博弈中占极少数;最后,证明了绝大多数的2人非合作有限博弈的任何策略矩阵均可以"重复剔除严格劣策略"原则化为方阵.Considering the mathematical structures,a feasible method to classify most 2-person noncooperative finite games was developed by Baire catalogue and measure.Firstly,it was proved that when one player chose a certain strategy and another had a unique optimal strategy under the Baire catalogue condition,this kind of games were majority.Secondly,it was proved that when one player chose a certain strategy and another had more than two optimal strategies under the measure condition,this kind of games were minority.Finally,it was proved that every strategy matrix of majority games could be transformed to square matrix by means of ＂rejecting strictly dominated strategy repeatly ＂.

关 键 词：2人非合作有限博弈 博弈分类 Baire纲 测度 

分 类 号：O177.91[理学—数学]