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Related Experiment Video

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

Asim Ghosh1, Arnab Chatterjee2, Anindya S Chakrabarti3

  • 1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
PubMed
Summary

This study models restaurant competition to explain city growth, finding that uniform fitness leads to a Zipf law for customer distribution. This model demonstrates how such laws emerge in city sizes.

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Area of Science:

  • Complex systems
  • Urban economics
  • Game theory

Background:

  • Cities exhibit complex growth and organization patterns.
  • Resource utilization and competition are key factors in urban development.
  • The emergence of statistical laws, like the Zipf law, in urban systems requires explanation.

Purpose of the Study:

  • To model resource utilization in a competitive scenario inspired by urban growth.
  • To investigate the emergence of the Zipf law in customer distribution among competing entities.
  • To explore the robustness of the Zipf law under varying fitness dynamics.

Main Methods:

  • Development of a game-theoretic model of restaurants competing for customers.
  • Utilizing an iterative learning process to simulate customer attraction.
  • Exact calculation of utilization fractions and analysis of steady-state fitness distributions.

Main Results:

  • Uniform fitness distribution among restaurants results in a Zipf law for customer numbers.
  • A modified model where fitness is dynamic and can be reset shows a power-law distribution for steady-state fitness.
  • The number of customers continues to follow the Zipf law even with dynamic fitness, indicating model robustness.

Conclusions:

  • The proposed model provides a paradigm for understanding the emergence of the Zipf law in city size distributions.
  • The Zipf law's persistence under dynamic fitness highlights the model's explanatory power for urban phenomena.
  • The study offers insights into the interplay of competition, learning, and fitness in shaping urban structures.