【作者】 张小琴；

【导师】 姚洪兴；

【作者基本信息】 江苏大学 ， 应用数学， 2007， 硕士

【摘要】 自从1998年以来,复杂网络就成为国内外各界学者研究的一个热点,其中复杂动态网络可以用来描述从生物到技术乃至社会各类开放复杂系统的构架。而博弈论是20世纪初就发展起来的一门学科,其中的演化博弈发展非常迅速。本文试图将复杂网络与博弈论知识结合起来,建立基于复杂网络的博弈模型,运用动力学等方法对模型进行分析,并研究其在员工流失管理中的应用。第一章简单介绍本课题研究的背景、现状及主要内容。第二章介绍复杂网络的基本概念和几个比较经典的网络模型,以及动力学、博弈论的基本知识。第三章进一步研究演化网络模型的度分布。通过对满足条件的主方程作傅里叶变换,对演化网络的度进行了精确求解,发现现实世界的演化网络中度指数大多数是大于2的,也有一少部分是小于2的,但不论网络如何演化,其度指数都在(1,4)这个范围内。第四章通过建立基于复杂网络的博弈模型对员工流失问题进行了研究。在重复博弈的条件下对其复制动态系统进行网络分析和稳定性分析,发现此模型中的系统在不同的参数影响下是处于动态平衡的,这从理论上对员工的流失管理提供了依据。第五章进一步研究国有企业中的员工流失问题。首先建立复杂网络上的博弈模型,在参与者不同的理性行为下对其进行博弈分析,然后对网络上的两类不同结点进行稳定性分析,从而得到网络在不同博弈条件下的演化机制:参与者的行动是基于对手的策略作出的,并且网络的结点是渐进稳定的。更多还原

【Abstract】 Since 1998, research on Complex networks has begun to be hotspot at home and abroad, and complex dynamic networks can be used to describe the framework of complex systems from biology to technology. While Game theory is a subject appeared in early 20th, and evolutionary game theory develops quickly. Complex networks is attempted to be combined with Game theory, a game model based on Complex networks is established and analysed making use of dynamic method, etc. Then its application in employees’ turnover management is studied in this paper.In Chapter 1, the background, current situation, contents and significance of the research are introduced briefly.In Chapter 2, basic concepts and several classical network models of Complex networks and elementary knowledge of Game theory and dynamics are introduced.In Chapter 3, degree distribution of evolving network model is studied again. Making Fourier transform to the main equation which accords with all the conditions, and solving the degree of evolving networks exactly, we can achieve conclusions that in real world networks, their degree exponents are almost more than 2, and minorityof theirs is less than 2, nevertheless, they are between (1,4).In Chapter 4, employees’ turnover is studied through establishing a game model based on Complex networks. The network and its stability are analysed under the condition that the game is repeated, we find that the system is dynamic stable under different parameters, which provides evidences for employees’ turnover management in theory.In Chapter 5, employees’ turnover in state corporations is studied. Firstly, a game model based on Complex networks is established and analysed use Game theory under the condition that the participants are rational, then two kinds of nodes’ stability are analysed, we get the conclusion that evolutionary mechanism of the network in different state is participants’ action is based on their rivals’ strategies, and the nodes are gradually stable.更多还原