破解“蜈蚣博弈”悖论：“灰数规整”顺推归纳法研究

中国管理科学 ›› 2008, Vol. 16 ›› Issue (1): 180-186.

破解“蜈蚣博弈”悖论：“灰数规整”顺推归纳法研究

方志耕, 刘思峰, 施红星, 徐正栋

南京航空航天大学经济与管理学院江苏南京210016

收稿日期:2007-05-23 修回日期:2007-12-21 出版日期:2008-02-28 发布日期:2008-02-28
作者简介:方志耕(1962- ),男(汉族),安徽人,南京航空航天大学经济与管理学院,教授,博士生导师,研究方向:管理工程、灰色系统理论.
基金资助:
国家自然科学基金项目(70473037、70701017);江苏省高等学校首批优秀科技创新团队;教育部哲学社会科学研究后期资助项目(07JHQ0053);灰色博弈理论及其应用研究;江苏省软科学研究基金项目(BR2007003、BR2007020);南京市软科学(200702008);南京市软科学招标项目(20060216);江苏省哲学社会科学基金项目成果(07EYA017);南京航空航天大学“十一五学科建设项目

Solving the Paradox of Centipede Game：A New Model of Grey Structured Algorithm of Forwards Induction

FANG Zhi-geng, LIU Si-feng, SHI Hong-xing, XU Zheng-dong

School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2007-05-23 Revised:2007-12-21 Online:2008-02-28 Published:2008-02-28

摘要/Abstract

摘要： 动态博弈分析的中心内容是子博弈完美纳什均衡分析,子博弈完美纳什均衡分析的核心方法是逆推归纳法^[1,2]。长期以来,逆推归纳法悖论与现实严重不符的现象困扰着学术界。本文揭示了逆推归纳悖论产生的根源:首先是其所犯的微观逻辑推理对整体宏观逻辑观忽略的错误;或者说只重视眼前(近期)利益,而忽略长远利益;其次是经典的多阶段动态博弈模型的结构形式无法满足人们对整体的和长远的利益考虑与均衡分析。本文构建了一种新型的基于未来博弈引导值的动态博弈模型的结构形式;设计了多阶段动态博弈的逆推"灰数规整"算法;构建多阶段动态博弈的"终止"和"引导"纳什均衡解的概念体系,并提供了方便有效的均衡分析方法;从而较好地破解了"蜈蚣博弈"的悖论。

关键词: 蜈蚣博弈, 灰数规整, “终止”纳什均衡, “引导”纳什均衡

Abstract: The main contacts of dynamic game analysis theories are sub-game perfect Nash equilibrium analysis,whose key method is backwards induction. Since a long time,it is so confused for academia that the backwards induction is definitely unsuitable with the fact. This paper reveals the origin of backwards induction:first of all,the micro logic is wrong for overall macro logic neglect. In other words,so meo ne focuses on recent interest rather than long interest. Secondly classic multi-stage model of the dynamic game structure cannot fit for the people to consider and balancedly analyze the overall and long interest. This paper constructs a modern structure based on the future dynamic game model and designs the backstepping grey structured algorithm of dynamic multi-stage game,constructs the termination and guide of the multistage dynamic game and offers the convenient and efficient balanced analysis and further explains the paradox of Centipede game.

Key words: Centipede game, grey structured algorithm, the termination and guide of the multi-stage dynamic game

中图分类号:

C931

方志耕, 刘思峰, 施红星, 徐正栋. 破解“蜈蚣博弈”悖论：“灰数规整”顺推归纳法研究[J]. 中国管理科学, 2008, 16(1): 180-186.

FANG Zhi-geng, LIU Si-feng, SHI Hong-xing, XU Zheng-dong. Solving the Paradox of Centipede Game：A New Model of Grey Structured Algorithm of Forwards Induction[J]. Chinese Journal of Management Science, 2008, 16(1): 180-186.