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

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

Abstract

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.

Suggested Citation

  • Asim Ghosh & Arnab Chatterjee & Anindya S. Chakrabarti & Bikas K Chakrabarti, 2014. "Zipf's law in city size from a resource utilization model," Papers 1403.1822, arXiv.org, revised Oct 2014.
    • Handle: RePEc:arx:papers:1403.1822
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    Cited by:

    1. Ghosh, Asim & Chatterjee, Arnab & Inoue, Jun-ichi & Chakrabarti, Bikas K., 2016. "Inequality measures in kinetic exchange models of wealth distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 465-474.
    2. Chatterjee, Arnab & Ghosh, Asim & Chakrabarti, Bikas K., 2017. "Socio-economic inequality: Relationship between Gini and Kolkata indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 583-595.
    3. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.
    4. Takeshi Kato & Yasuyuki Kudo & Hiroyuki Mizuno & Yoshinori Hiroi, 2020. "Regional Inequality Simulations Based on Asset Exchange Models with Exchange Range and Local Support Bias," Applied Economics and Finance, Redfame publishing, vol. 7(5), pages 10-23, September.
    5. Ikeda, Kiyohiro & Murota, Kazuo & Takayama, Yuki & Kamei, Motohiro, 2016. "Group-theoretic spectrum analysis of hexagonal city distributions in Southern Germany and Eastern USA," MPRA Paper 74567, University Library of Munich, Germany.
    6. Jonathan D. Wren & Constantin Georgescu, 2022. "Detecting anomalous referencing patterns in PubMed papers suggestive of author-centric reference list manipulation," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(10), pages 5753-5771, October.
    7. Lee, Ji-Hye & Jo, Junghyo & Kim, Jong Won & Lee, Keumsook & Choi, M.Y., 2022. "Spatial distributions of restaurants emerging from pedestrian behavior and online information sharing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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