双向生产者-消费者网络与企业规模分布
Bipartite Producer-Consumer Networks and the Size Distribution of Firms
摘要：
构造了一个二分的生产者-消费者网络来描述产业结构。从消费者到生产者的边表示消费者对最终产品的选择，生产者的程度可以表示其市场份额。因此，企业的规模分布可以用生产者的程度分布来表征。生产者接受新消费的概率取决于其初始吸引力描述的竞争能力和偏好依恋描述的竞争中的自我强化机制。研究了总消费量不变和市场增长的情况。结果表明：1、在没有市场增长和统一的初始吸引力$a$的情况下，企业规模的最终分布对于$a>1$是Gamma分布，对于$a=1$是指数分布。如果是$a<1$，则在小规模时服从幂律分布，在上尾时服从指数分布; 2、对于成长市场，企业规模分布服从幂律分布。该指数受市场增长和企业初始吸引力的影响。
英文摘要：
A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degree distribution. The probability for a producer receiving a new consumption is determined by its competency described by initial attractiveness and the self-reinforcing mechanism in the competition described by preferential attachment. The cases with constant total consumption and with growing market are studied. The following results are obtained: 1, Without market growth and a uniform initial attractiveness $a$, the final distribution of firm sizes is Gamma distribution for $a>1$ and is exponential for $a=1$. If $a<1$, the distribution is power in small size and exponential in upper tail; 2, For a growing market, the size distribution of firms obeys the power law. The exponent is affected by the market growth and the initial attractiveness of the firms.
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