【作者】 李一啸；

【导师】 孔繁胜； 金小刚；

【作者基本信息】 浙江大学 ， 计算机科学与技术， 2010， 博士

【摘要】 社会—经济系统结构和动力学分析和建模是复杂系统研究的重要课题。近年来复杂网络研究兴起,自然界和人类社会中结构不规则、复杂的、时间上动态演化的网络成为关注热点。大量分析表明真实社会、经济网络表现出丰富的复杂网络结构特征,从而为社会—经济系统结构建模提供了新的实证依据。演化博弈理论主要通过数学建模、计算机模拟等方法对合作演化的动力学过程进行建模和分析。社会—经济系统中存在广泛的合作,将演化博弈理论应用于该系统中合作演化的动力学研究具有重要理论意义和实际指导作用。尽管该研究取得了令人瞩目的成果,然而由于社会—经济系统的复杂性,仍存在大量问题亟待探索,例如复杂网络结构、人类多样性的行为策略等因素对于合作演化的影响作用。本文以复杂网络和演化博弈理论为基础,综合运用图论、微分方程、基于Agent模拟等多学科领域知识,以社会—经济系统作为研究对象,围绕两个中心主题进行研究：由网络表达的系统结构以及系统中合作演化的动力学过程。一方面,本文研究了如何对具有社区结构特征的大规模社会网络进行建模,提出了一个具有社区结构特征的网络模型；另一方面,本文研究了如何对社会—经济系统中合作演化的动力学进行建模,考察人类多样性的行为策略、策略更新规则、复杂网络结构等因素的影响作用,研究路线从引入其他行为策略的演化博弈(无网络结构)到规则网络上的演化博弈,最后到复杂网络上的演化博弈。论文主要研究工作和创新点如下：1.提出了一个具有社区结构特征的社会网络模型,并给出了相应的人工网络生成算法。本文研究了如何对具有社区结构特征的社会网络进行建模。考虑了社会网络节点的社会性,定义了社会距离,将基于社会相似度连接等机制加入B-A无尺度网络模型,得到了一个较好描述社会系统结构的社会网络模型。数值分析和模拟表明,该网络模型不仅保持了B-A模型的无尺度分布特征,还具有可调的社区强度和聚集度系数特征。2.研究了再分配行为在演化博弈过程中对于合作演化的影响作用。结合当前人类行为研究的热点,将一般的再分配行为引入基本的演化博弈模型,形成了一个两阶段的共生演化模型。以公共品博弈为例,采用群体动力学和基于Agent动力学的方法对该模型进行了研究,给出了系统达到存在一定比例合作的稳定均衡的途径,揭示了再分配行为对于合作演化的影响作用。3.研究了规则网络上的演化博弈中由于不同策略更新规则导致的合作演化的结果差异。考虑了策略更新规则的划分,定义了时序比例和阈值比例来分别刻画时序规则和选择规则。通过模拟规则格网上的合作演化,发现选择规则对于导致合作产生的损失收益比的参数范围的影响作用非常明显。一般地,阈值选择在网络上的演化博弈中能够有效地增大导致合作产生的损失收益比的参数范围。4.研究了R-B层次网络模型上的演化博弈并给出了一种提高合作水平的模型改进方法。为研究复杂网络结构特征对演化博弈过程中合作的影响作用,模拟了R-B模型上的演化博弈动力学过程。通过与B-A模型比较,验证了中心节点互联结构是导致复杂网络上的演化博弈中高水平和强稳定性合作的一个因素的结论。对R-B模型进行了改进,将少量的中心节点进行了互联,同时保持了层次网络的基本统计特性。对改进后的R-B模型上的演化博弈模拟后发现,合作水平提高。更多还原

【Abstract】 Some important issues for the study of complex systems are analyzing and modeling the structure and the dynamics of socio-economic systems. Recently, with the rise of the study of complex networks, networks in both nature and human societies, whose structure is irregular, complex and dynamically evolving in time, attract great research interest. A lot of analyses show that social and economic networks from the real world exhibit rich structure characteristics of complex networks, thereby providing new empirical foundations for modeling socio-economic systems. Evolutionary game theory focuses on modeling and analyzing the dynamics of the evolution of cooperation using methods of mathematical modeling, computer simulation, etc. Socio-economic systems are characteristic of extensive cooperation and it is of important theoretical significance and guiding function for solving real problems to apply evolutionary game theory to studying the evolution of cooperation in these systems. Though fruitful results have been achieved in this area, there are still many questions due to the complexity of socio-economic systems, such as the influences of_complex network structure, diverse human behaviors, and other factors.Based on theories of complex network and evolutionary game, this dissertation focuses on socio-economic systems and studies two central topics, i.e. their structure represented by networks and their dynamics of the evolution of cooperation, synthetically using methods of multiple disciplines, such as graph theory, differential equation, Agent-based simulation, etc. On one hand, this dissertation studies how to model large-scale social networks with community structure and proposes a new network model with community structure; on the other hand, this dissertation studies how to model the dynamics of the evolution of cooperation in socio-economic systems, by investigating the effects of diverse human behaviors, strategy update rules, complex network structure, following the research path from evolutionary games with other human behaviors (no network structure) to evolutionary games on regular networks and evolutionary games on complex networks. The main results and contributions of this dissertation are as follows.1. A social network model with community structure is proposed and the corresponding algorithm is provided. How to model large social networks with community structure is studied in this dissertation. By considering the sociality of nodes in social networks, social distance is defined and the mechanisms of linking via social similarity and triad formation are added into B-A scale-free network model. Both numeric analysis and simulation show that this network model not only maintains the property of scale-free degree distribution, but it has tunable strength of community structure and clustering coefficient.2. The effect of redistribution behaviors upon the evolution of cooperation in evolutionary game dynamics is investigated. Inspired by recent advancement in the interdisciplinary study of human behaviors, the general behavior of redistribution is introduced into the basic model of evolutionary game and a two-stage co-evolutionary model is formed. As an example, the co-evolutionary model with public goods game is analyzed using both methods of population dynamics and Agent-based dynamics. The approach to achieve stable equilibrium with a certain proportion of cooperation for the systems is presented and the influence of redistribution behaviors on the evolution of cooperation is revealed.3. The different results for evolutionary games on regular networks caused by different strategy update rules are studied. By considering the classification of strategy update rules, synchronization proportion and threshold proportion are defined to describe synchronization rules and threshold rules, respectively. By simulating the evolution of cooperation on regular lattice, it is found that selection rules have a great effect upon the range of cost-to-benefit ratio for cooperation. Generally, threshold selection rule enlarges the range of cost-to-benefit ratio for cooperation in the processes of evolutionary games on networks.4. Evolutionary games on R-B hierarchical network model are studied and a way of modifying the model to increase cooperation level is presented. To study the influence of structure characteristics on cooperation in evolutionary game dynamics, the dynamics of evolutionary games on R-B model is simulated. By comparing the result of R-B model with that of B-A model, it is verified that interconnection between hub nodes is one factor for high-level and robust cooperation in evolutionary games on complex networks. R-B model is modified by interconnecting a few hub nodes and basic statistical characteristics of hierarchical networks are maintained. After simulating the dynamics of evolutionary games on modified R-B model, it is found that cooperation level increases.更多还原