Zipf's law in city size from a resource utilization model.
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, it gives rise to a Zipf law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness. A variant of the model is also introduced where the fitness can be treated as an ability to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, while the distribution of the number of customers still follows the Zipf law, implying the robustness of the model. Our model serves as a paradigm for the emergence of Zipf law in city size distribution.
Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India.
Asim
A
Ghosh
Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India and BECS, Aalto University School of Science, P.O. Box 12200, FI-00076, Finland.
Arnab
A
Chatterjee
Department of Economics, Boston University, 270 Bay State Road, Boston, Massachusetts 02134, USA.
Anindya S
AS
Chakrabarti
Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India and Economic Research Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India.
Bikas K
BK
Chakrabarti