连续对策的最大熵策略密度对策解  

STRATEGY DENSITY SOLUTIONS WITH GREATEST ENTROPY OF A CONTINUOUS GAME

作　　者：姜殿玉[1] 

机构地区：[1]淮海工学院对策论及其应用研究所,连云港222005

出　　处：《系统科学与数学》2008年第9期1158-1172,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助课题(78970025);江苏省高校自然科学研究计划项目(05KJD110027).

摘　　要：对于正方形[0,2]×[0,2]上的连续对策,将局中人的非纯策略(概率分布函数)的导数称为这个局中人的策略密度(概率密度函数).建立了这种连续对策的最大熵理论.主要证明了当每个局中人都没有最优纯策略时,具有最大熵的最优策略密度集合的非空紧凸性,研究了最优策略密度的最大熵,给出一类带有最大熵的连续对策.For a continuous game on a square [0,2] × [0,2], derivative of a player＇s non-pure strategy （a probability distribution function） is called the player＇s strategy density （a probability density function）. In this paper studies, the theory of greatest entropy of the continuous game is considered. It is proved that if each player has no optimal pure strategy, then set of optimal strategy densities is a nonempty compact convex set. The greatest entropy of optimal strategy densities is studied, and a continuous game with the greatest entropy is given.

关 键 词：运筹学 连续对策 策略密度 最大熵 

分 类 号：O225[理学—运筹学与控制论]