【作者】 刘凌；

【导师】 魏蛟龙；

【作者基本信息】 华中科技大学 ， 通信与信息系统， 2011， 硕士

【摘要】 20世纪末,复杂网络取得了高速的发展,复杂网络广泛应用于经济学、生物科学、信息科学等各个领域。而在博弈论中引入复杂网络,为研究群体中个体之间的行为建立了一个极好的框架。复杂网络上的博弈主要围绕两个方面:网络拓扑结构和策略选择机制展开研究。本文针对经典的囚徒困境博弈,分别从网络拓扑结构以及博弈个体的策略选择机制出发,对复杂网络上的囚徒困境博弈进行了介绍。首先介绍了复杂网络上的博弈的两个基础理论:复杂网络和博弈论。针对复杂网络介绍了复杂网络理论的发展、描述网络特性的网络参数和复杂网络模型。而对博弈论则介绍了博弈理论发展、Nash均衡、囚徒困境博弈以及演化博弈。然后介绍了囚徒困境博弈下的两种不同策略选择机制:基于模仿学习和基于记忆的自我学习机制。并在复杂网络上提出了一种新的动态拓扑囚徒困境博弈算法,该算法使网络在博弈过程中拓扑结构也在不断变化,实现了网络拓扑和博弈动力学的共演化。并用Matlab进行仿真,采用动态拓扑博弈算法时,发现如下结果:网络节点度的最大值变小,且度最大值随着背叛诱惑值增大而减小;大于网络平均度的节点数增多;在采用基于记忆自我学习机制时,度数为1的节点的合作比趋向于0,度大于1的节点的合作比趋向于1;在采用基于模仿学习机制时,与静态拓扑的囚徒困境博弈相比,动态拓扑囚徒困境博弈算法网络的合作水平较高。最后对全文作了总结,并对以后的工作进行了展望。更多还原

【Abstract】 In the 20th century, complex network have made a rapid development. The complex networks are widely used in many different fields, such as economics, biological sciences, information science and so on. By introducing complex network to game theory, a perfect frame on which we can study the behavior of individuals on networks is established. The research of the game on complex networks has two main points: network topology and the learning mechanism of individual on complex networks.Based on the above two points: network topology and the learning mechanism of individual on complex networks. This paper introduced the Prisoner’s Dilemma Game (PDG) on complex networks.First we introduced two basic theories of the game on complex networks: complex networks and game theory. To complex networks, we review the development of complex networks, some network parameters and some typical network structures. And we also studied something about game theory, including the development of game theory, Nash Equilibrium, Prisoner’s Dilemma Game (PDG), and Evolutionary Game.Then two different learning mechanisms of individual on complex networks: the learning mechanism of imitating the strategy of neighbors and the learning mechanism based on historical memory. A Prisoner’s Dilemma Game (PDG) Model based on Dynamic topology (PDG-DT) was proposed, in this model the network topology is changed while the game is going on, so the network topology and the strategy of individuals have a co-evolutionary. Matlab software are used to simulate. When we do simulation under the PDG-DT model, we found the result as follows. The maximum degree of network nodes is smaller than that of initial network nodes, and as the value of temptation become higher the maximum get lower; the number of nodes whose degree is larger than average degree of network nodes become greater; when the network uses the learning mechanism based on historical memory, the cooperation level of nodes whose degree equals 1 trend to be 0, and the cooperation level of nodes whose degree is greater than 1 approach to be 1; when the network uses the learning mechanism of imitating the strategy of neighbors, compare to Prisoner’s Dilemma Game (PDG) Model based on Static topology (PDG-ST), the network under the PDG-DT model can get a higher level of cooperation.At last, the entire work is reviewed and outlook of this thesis is made.更多还原