2005/07/21 by Wang Dahui, Zhou Li, Zengru Di +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · Social Sciences · #Attractiveness #Business #Combinatorics #Competition (biology) #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Complex network #Computer science #Constant (computer programming) #Consumption (sociology) #Degree distribution #Distribution (mathematics) #Econometrics #Economics #Evolutionary Game Theory and Cooperation #Exponent #Exponential distribution #Market power #Market share #Marketing #Matching (statistics) #Mathematics #Microeconomics #Production (economics) #Statistics #physics.soc-ph #q-fin.GN
paper · pdf · doi:10.1016/j.physa.2005.08.006
13 pages, 3 figures
arxiv created 2005/07/21 · openalex publication_date 2005/09/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.