Zipf's law in city size from a resource utilization model

Research output: Contribution to journalArticleScientificpeer-review


  • Asim Ghosh
  • Arnab Chatterjee
  • Anindya S. Chakrabarti
  • Bikas K. Chakrabarti

Research units

  • Saha Institute of Nuclear Physics
  • Boston University
  • Indian Statistical Institute


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.


Original languageEnglish
Article number042815
Number of pages7
JournalPhysical Review E
Issue number4
Publication statusPublished - 27 Oct 2014
MoE publication typeA1 Journal article-refereed

ID: 9516070