博弈的统计演化分析

数学物理学报

博弈的统计演化分析

龚小庆

浙江工商大学统计与计算科学学院杭州 310035

收稿日期:2004-02-09 修回日期:2005-09-30 出版日期:2006-10-25 发布日期:2006-10-25
通讯作者: 龚小庆
基金资助:
国家自然科学基金(60174048, 70271076)资助

Statistical Analysis on Evolutionary Behaviors of Games

Gong Xiaoqing

Department of Statistics, Zhejiang Gongshang University, Hangzhou 310035

Received:2004-02-09 Revised:2005-09-30 Online:2006-10-25 Published:2006-10-25
Contact: Gong Xiaoqing

摘要/Abstract

摘要： 首先定义了具有确定分布的随机环境中的基于适应度的平均选择算子,然后证明了主体战略集上的任一概率密度在平均选择算子的迭代过程中收敛于平均适应度函数的最大集上的某一分布,
然后就多主体的博弈问题定义了平均选择算子,并以此为基础证明了平均选择算子的不动点就是博弈的纳什均衡.

关键词: 平均选择算子, 概率分布演化, 纳什均衡

Abstract: Average selection operators in random environments are introduced in the first place, and it is proved that the sequence of probability distributions in agents' strategies set, when repeatedly operated by average selection operator, converges to the probability distribution in the subset of strategies that takes the largest value of average fitness. Then, the concept of average selection operator is extended to the multi-agents game problems, and it is
proved that the fixed points of such an operator are just the Nash equilibria of games.

Key words: Average selection operators, Evolution of probability distribution, Nash equilibrium

中图分类号:

91A22

龚小庆. 博弈的统计演化分析[J]. 数学物理学报, 2006, 26(5): 747-752.

Gong Xiaoqing. Statistical Analysis on Evolutionary Behaviors of Games[J]. Acta mathematica scientia,Series A, 2006, 26(5): 747-752.