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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/294

Title: A model for the size distribution of customer groups and businesses
Authors: Zheng, DG
Rodgers, GJ
Hui, PM
Keywords: Disordered systems and neural networks
Statistical mechanics
Publication Date: 2002
Publisher: Elsevier
Citation: Physica A, 310: 480-486
Abstract: We present a generalization of the dynamical model of information transmission and herd behavior proposed by Eguiluz and Zimmermann. A characteristic size of group of agents s0 is introduced. The fragmentation and coagulation rates of groups of agents are assumed to depend on the size of the group. We present results of numerical simulations and mean field analysis. It is found that the size distribution of groups of agents ns exhibits two distinct scaling behavior depending on s ≤ s0 or s > s0. For s ≤ s0, ns ∼ s-(5/2 + δ), while for s > s0, ns ∼ s-(5/2 -δ), where δ is a model parameter representing the sensitivity of the fragmentation and coagulation rates to the size of the group. Our model thus gives a tunable exponent for the size distribution together with two scaling regimes separated by a characteristic size s0. Suitably interpreted, our model can be used to represent the formation of groups of customers for certain products produced by manufacturers. This, in turn, leads to a distribution in the size of businesses. The characteristic size s0, in this context, represents the size of a business for which the customer group becomes too large to be kept happy but too small for the business to become a brand name.
URI: http://bura.brunel.ac.uk/handle/2438/294
http://www.sciencedirect.com/science/article/pii/S0378437102008026
DOI: http://dx.doi.org/10.1016/S0378-4371(02)00802-6
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers
Mathematical Physics

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