基于复杂网络的财富分布与财富演化分析
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摘要
贫富差距既是一个基本的经济问题,又是一个突出的社会问题,对社会稳定有着复杂的多重影响。合理有效的收入分配制度应该具有公正性、公平性、合理性。收入分配制度的制定在一定程度上是由社会结构来决定的,而社会经济关系又是社会结构的主要内容之一。每个人或组织的经济行为都受制于其所在的经济关系网络,其具有复杂性、整体性、层次性、动态性等重要特征。因此通过社会经济关系来认识收入和财富分配不平等的问题是十分必要且具有现实意义的。尤其随着复杂网络的兴起,经济学家逐渐认识到现实的经济系统中往往存在着巨大而复杂的网络结构。而传统的经济学理论假设财富交易模型是一个封闭的、守恒的系统,忽略了社会经济关系的结构。因此在复杂网络模型研究的基础上,通过经济关系结构对财富分配的不均衡性的影响进行比较、研究和综合概括就显得尤为重要。本文主要的内容概述如下：
1.讨论了不同社会经济关系结构对财富分布的影响。
社会经济关系的结构属性与个体拥有的财富量是息息相关的,尤其是社会经济关系结构的动态增长性。据此,本文分析了具有动态增长性的经济关系结构对财富分布的影响。首先,在相同的交易机制下,采用经典的复杂网络模型刻画了一般的社会经济关系,分析了不同的社会关系结构下财富分布的形式。通过数值仿真和算例分析得出,无标度网络下高收入者的财富分布是符合Pareto分布的,与中低收入者的分布形式是不同的,其与现实社会中的财富分布形式是相符的。其次,考虑到实际经济活动中存在对已有合作的维持或是解除,以及新合作项目的开发等一系列经济活动,建立了一个基于边动态变化的财富网络演化模型。通过计算机仿真,分析得到网络模型的度分布以及参数对财富分布均衡性的影响。
2.构造了两类动态网络财富演化模型。
影响财富分布的因素有许多,除了社会经济关系的结构特性,还有许多经济活动过程中特有的现象也会导致财富分布极不均衡,例如信息不对称性以及财富的流动性等。本文采用适当的网络模型刻画社会经济关系,改进了网络中择优连接准则,构造了两类动态网络财富演化模型。第一类模型称为IALN模型。该模型采用局域的概念来描述经济活动过程中信息不对称性的特点。新个体加入网络时,由于自己的知识有限且不对称,该个体会从自己所熟知的局域范围内选择合作个体进行交易,且每次交易转移的财富值不同,这均是个体信息的不对称性导致的结果。通过模拟仿真,给出了网络结构的相关参数与财富分布以及基尼系数的关系图,分析可知网络中节点度对累积财富值的影响非常大,基本上呈线性关系。第二类模型称为RDN模型。该模型通过财富流动性的特点引入了财富重分机制,同时为达到调节网络结构的目的引入了影响力系数。通过理论推导得出财富总值、节点的连接度以及累积财富值的时变方程。然后,采用数值仿真,得到不同参数下的财富分布规律、基尼系数的变化以及连接度与累积财富值之间的关系图。最后,对IALN与RDN在实际社会中的应用背景进行了探讨。
3.结合收益以及收益分配等问题构造了一类财富演化模型。
收益是个体和机构进行经济活动的主要目标,也是人类社会关系最有利的动机之一,是经济活动中不可忽视的因素。首先,木章考虑了局域择优连接和局部财富重新分配,并且将收益函数以及收益分配引入到模型中,构建了一个基于收益的财富演化网络模型。其次,运用率方程方法,推导出了节点度以及节点财富值的动力学方程。最后,从结构与财富两个方面对网络特性以及财富分布的均衡性进行了分析。研究结果表明,节点的度分布服从幂律分布,而财富分布是服从双幂律分布的。且该网络是一个负向匹配网络,度较小的节点的邻居之间关系极为紧密,极易形成集团。通过对富分分布以及财富熵的分析可知,该网络中财富分布极不均衡。不同的参数下,个体间所表现出的财富异质性也不相同。
4.建立了一个基于群异质性的产业群合作网络。
本文将个体和个体之间的相互作用模型推广到个体与组织以及组织与组织之间的网络联结中。首先,构建了一个基于群异质性的产业群合作网络,并将社会网络中的基本性质推广到群间的定义。其次,应用群网络的结构参数定量刻画了群的异质性,并采用柯布—道格拉斯函数对其进行分析。结果表明,群间成本与所占共享资源比重这两者是呈反比的。最后,通过计算机仿真,对模型的网络结构特征值进行了模拟验证。分析可得,该群网络是一个非均匀网络,其集中度与群聚集度都非常低,这与林南在社会资源理论中提出的弱关系理论是一致的。
As a basic economic problem, the gap between poor and rich is an outstanding social problem. It has a complicated and multiple effects. Reasonable and effective income distribution should be impartiality, fairness and rationality. To a certain extent, the system of income distribution is decided by the social structure of which the social economic relationship is the main content. The economic activities of everyone or organization are all dominated by their own economic relationship network which has complexity, wholeness, hierarchy, dynamic and other important characteristics. So, it is very necessary and realistic to realize the unequal distribution of income and wealth by the way of the structure of social economic relationship. Especially the developing of complex network, economists come to realize that the real economic systems always have a large and complex network formation which is neglected by previous studies. But trading models are always proposed to be closed and conservation systems. So, under the banner of complex network, it is particularly important to compare, study and comprehensive summary the impacts of anisotropic wealth distribution through the economic relationship structure. The main contents in this paper can be summarized as follows:
1. The influences of different social economic relationship structure on wealth distribution are discussed.
The amount of agent's wealth is closed linked to the structural properties of social economic relationship structure which is especially the property of dynamic growing. Based on this point, we analyze the impact on the wealth distribution by the economic relationship structure with dynamic increasing character. First, under the same trading mechanism, the forms of wealth distribution are given under the different social economic relationship structures which are depicted by the classic complex network models. By methods of simulation and numerical example, it is obtained that the wealth distribution of richer in BA scale network follows Pareto distribution which is different to the others'. So. the wealth distribution in BA scale network is consistent with that of real society. Then, a wealth evolving network model is built based on the phenomenon of links dynamic change, which is considered a series of economic activity in the actual economic activity, such as keeping or removing existing cooperation and developing new cooperation and so on. The degree distribution and the balance of wealth distribution which is influenced by different parameters are analysis obtained by the way of simulation.
2. Two types of wealth dynamic evolution network models are constructed.
There are many factors that can lead to the unequal wealth distribution. In addition to the structure characters of social economic relationship, there are still many economical pheromones such as information asymmetry and the liquidity of wealth and so on. We adopt appropriated network model to describe the social economic relationship, and improve the preferred probability. So, two kinds of model are given in this part. The first kind of model is known as IALN. The concept of local is used to descript the information asymmetry during the trading process. When the new node is added to the network, it will select cooperated agent from the scale which it is familiar with nodes because of their limited and asymmetric knowledge. As the same reason, the transaction value which is different is preestablished. This also can reflect the character of asymmetric knowledge. By simulation, figures of the relationship between structural parameters with wealth distribution and gini coefficient are given. Through analysis, we obtained that the impact on the wealth distribution by the node degree is very big. basically in a linear relationship. The second kind of model is called RDN. An evolving network model is induced by the mechanism of wealth redistribution which is introduced by the liquidity of wealth. An influenced coefficient which is in order to achieve the purpose of adjusting the network structure is defined. By applying the theoretical deduction, the time-varying equation of the total wealth, the degree and cumulated wealth are obtained. Then, by the method of simulation, the wealth distribution, the gini coefficient and the relationship figures between node degree and cumulated wealth are given based on the different values of parameters. Finally, application background analysis in actual society is discussed.
3. An evolving network model induced by the wealth is proposed, which is considered the earning and income distribution.
Profit is one of the main targets of individuals and organizations in economic activities. It is also one of most beneficial motivation of human social relationship. It is always a factor that can not be ignored during economic activities. Firstly, an evolving wealth network model is constructed which not only considered the local preferred link and local wealth redistribution but also earning and income distribution. Secondly, Using rate equations, the dynamic equations of degree and wealth distributions are obtained. Finally, we analyze the model from the two aspects of structure and wealth. The results indicate that the node degree follows the power law distribution; however the wealth distribution fits double power law distribution. It is obtained that the wealth model is a negative network, in which the nodes with small degree display relatively greater clustering. By analyzing the wealth distribution and wealth entropy, we investigate the social wealth distribution is unbalanced. The wealth heterogeneity between agents is still different.
4. An industrial clusters cooperation network model is build based on the heterogeneity of clusters.
The interaction models between agents can be extended to models which interact between agent and organization or between different organizations. Firstly, an industrial clusters cooperation network model based on the heterogeneity is given. Meanwhile, the basic properties of social network are generalized to definition of clusters. Secondly, we quantitatively defined the difference degree between clusters by the parameters of cluster structure. The degree of clusters heterogeneity can be analyzed by Cobb-Douglas production function. The result manifests that the cost between different clusters is inversely proportional to the account of shared resource. Finally, the structure characteristic values of network can be verified by the computer simulation. By analysis, we obtain that the cluster network model is a heterogeneous network which the centrality and the clustering are very low. It is consent with the weak ties theory in the theory of social resources which is proposed by Lin Nan.
1.讨论了不同社会经济关系结构对财富分布的影响。
社会经济关系的结构属性与个体拥有的财富量是息息相关的,尤其是社会经济关系结构的动态增长性。据此,本文分析了具有动态增长性的经济关系结构对财富分布的影响。首先,在相同的交易机制下,采用经典的复杂网络模型刻画了一般的社会经济关系,分析了不同的社会关系结构下财富分布的形式。通过数值仿真和算例分析得出,无标度网络下高收入者的财富分布是符合Pareto分布的,与中低收入者的分布形式是不同的,其与现实社会中的财富分布形式是相符的。其次,考虑到实际经济活动中存在对已有合作的维持或是解除,以及新合作项目的开发等一系列经济活动,建立了一个基于边动态变化的财富网络演化模型。通过计算机仿真,分析得到网络模型的度分布以及参数对财富分布均衡性的影响。
2.构造了两类动态网络财富演化模型。
影响财富分布的因素有许多,除了社会经济关系的结构特性,还有许多经济活动过程中特有的现象也会导致财富分布极不均衡,例如信息不对称性以及财富的流动性等。本文采用适当的网络模型刻画社会经济关系,改进了网络中择优连接准则,构造了两类动态网络财富演化模型。第一类模型称为IALN模型。该模型采用局域的概念来描述经济活动过程中信息不对称性的特点。新个体加入网络时,由于自己的知识有限且不对称,该个体会从自己所熟知的局域范围内选择合作个体进行交易,且每次交易转移的财富值不同,这均是个体信息的不对称性导致的结果。通过模拟仿真,给出了网络结构的相关参数与财富分布以及基尼系数的关系图,分析可知网络中节点度对累积财富值的影响非常大,基本上呈线性关系。第二类模型称为RDN模型。该模型通过财富流动性的特点引入了财富重分机制,同时为达到调节网络结构的目的引入了影响力系数。通过理论推导得出财富总值、节点的连接度以及累积财富值的时变方程。然后,采用数值仿真,得到不同参数下的财富分布规律、基尼系数的变化以及连接度与累积财富值之间的关系图。最后,对IALN与RDN在实际社会中的应用背景进行了探讨。
3.结合收益以及收益分配等问题构造了一类财富演化模型。
收益是个体和机构进行经济活动的主要目标,也是人类社会关系最有利的动机之一,是经济活动中不可忽视的因素。首先,木章考虑了局域择优连接和局部财富重新分配,并且将收益函数以及收益分配引入到模型中,构建了一个基于收益的财富演化网络模型。其次,运用率方程方法,推导出了节点度以及节点财富值的动力学方程。最后,从结构与财富两个方面对网络特性以及财富分布的均衡性进行了分析。研究结果表明,节点的度分布服从幂律分布,而财富分布是服从双幂律分布的。且该网络是一个负向匹配网络,度较小的节点的邻居之间关系极为紧密,极易形成集团。通过对富分分布以及财富熵的分析可知,该网络中财富分布极不均衡。不同的参数下,个体间所表现出的财富异质性也不相同。
4.建立了一个基于群异质性的产业群合作网络。
本文将个体和个体之间的相互作用模型推广到个体与组织以及组织与组织之间的网络联结中。首先,构建了一个基于群异质性的产业群合作网络,并将社会网络中的基本性质推广到群间的定义。其次,应用群网络的结构参数定量刻画了群的异质性,并采用柯布—道格拉斯函数对其进行分析。结果表明,群间成本与所占共享资源比重这两者是呈反比的。最后,通过计算机仿真,对模型的网络结构特征值进行了模拟验证。分析可得,该群网络是一个非均匀网络,其集中度与群聚集度都非常低,这与林南在社会资源理论中提出的弱关系理论是一致的。
As a basic economic problem, the gap between poor and rich is an outstanding social problem. It has a complicated and multiple effects. Reasonable and effective income distribution should be impartiality, fairness and rationality. To a certain extent, the system of income distribution is decided by the social structure of which the social economic relationship is the main content. The economic activities of everyone or organization are all dominated by their own economic relationship network which has complexity, wholeness, hierarchy, dynamic and other important characteristics. So, it is very necessary and realistic to realize the unequal distribution of income and wealth by the way of the structure of social economic relationship. Especially the developing of complex network, economists come to realize that the real economic systems always have a large and complex network formation which is neglected by previous studies. But trading models are always proposed to be closed and conservation systems. So, under the banner of complex network, it is particularly important to compare, study and comprehensive summary the impacts of anisotropic wealth distribution through the economic relationship structure. The main contents in this paper can be summarized as follows:
1. The influences of different social economic relationship structure on wealth distribution are discussed.
The amount of agent's wealth is closed linked to the structural properties of social economic relationship structure which is especially the property of dynamic growing. Based on this point, we analyze the impact on the wealth distribution by the economic relationship structure with dynamic increasing character. First, under the same trading mechanism, the forms of wealth distribution are given under the different social economic relationship structures which are depicted by the classic complex network models. By methods of simulation and numerical example, it is obtained that the wealth distribution of richer in BA scale network follows Pareto distribution which is different to the others'. So. the wealth distribution in BA scale network is consistent with that of real society. Then, a wealth evolving network model is built based on the phenomenon of links dynamic change, which is considered a series of economic activity in the actual economic activity, such as keeping or removing existing cooperation and developing new cooperation and so on. The degree distribution and the balance of wealth distribution which is influenced by different parameters are analysis obtained by the way of simulation.
2. Two types of wealth dynamic evolution network models are constructed.
There are many factors that can lead to the unequal wealth distribution. In addition to the structure characters of social economic relationship, there are still many economical pheromones such as information asymmetry and the liquidity of wealth and so on. We adopt appropriated network model to describe the social economic relationship, and improve the preferred probability. So, two kinds of model are given in this part. The first kind of model is known as IALN. The concept of local is used to descript the information asymmetry during the trading process. When the new node is added to the network, it will select cooperated agent from the scale which it is familiar with nodes because of their limited and asymmetric knowledge. As the same reason, the transaction value which is different is preestablished. This also can reflect the character of asymmetric knowledge. By simulation, figures of the relationship between structural parameters with wealth distribution and gini coefficient are given. Through analysis, we obtained that the impact on the wealth distribution by the node degree is very big. basically in a linear relationship. The second kind of model is called RDN. An evolving network model is induced by the mechanism of wealth redistribution which is introduced by the liquidity of wealth. An influenced coefficient which is in order to achieve the purpose of adjusting the network structure is defined. By applying the theoretical deduction, the time-varying equation of the total wealth, the degree and cumulated wealth are obtained. Then, by the method of simulation, the wealth distribution, the gini coefficient and the relationship figures between node degree and cumulated wealth are given based on the different values of parameters. Finally, application background analysis in actual society is discussed.
3. An evolving network model induced by the wealth is proposed, which is considered the earning and income distribution.
Profit is one of the main targets of individuals and organizations in economic activities. It is also one of most beneficial motivation of human social relationship. It is always a factor that can not be ignored during economic activities. Firstly, an evolving wealth network model is constructed which not only considered the local preferred link and local wealth redistribution but also earning and income distribution. Secondly, Using rate equations, the dynamic equations of degree and wealth distributions are obtained. Finally, we analyze the model from the two aspects of structure and wealth. The results indicate that the node degree follows the power law distribution; however the wealth distribution fits double power law distribution. It is obtained that the wealth model is a negative network, in which the nodes with small degree display relatively greater clustering. By analyzing the wealth distribution and wealth entropy, we investigate the social wealth distribution is unbalanced. The wealth heterogeneity between agents is still different.
4. An industrial clusters cooperation network model is build based on the heterogeneity of clusters.
The interaction models between agents can be extended to models which interact between agent and organization or between different organizations. Firstly, an industrial clusters cooperation network model based on the heterogeneity is given. Meanwhile, the basic properties of social network are generalized to definition of clusters. Secondly, we quantitatively defined the difference degree between clusters by the parameters of cluster structure. The degree of clusters heterogeneity can be analyzed by Cobb-Douglas production function. The result manifests that the cost between different clusters is inversely proportional to the account of shared resource. Finally, the structure characteristic values of network can be verified by the computer simulation. By analysis, we obtain that the cluster network model is a heterogeneous network which the centrality and the clustering are very low. It is consent with the weak ties theory in the theory of social resources which is proposed by Lin Nan.
引文
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