Agent-Based Models of Geographical Systems

pp 677-704


Beyond Zipf: An Agent-Based Understanding of City Size Distributions

  • Timothy R. GuldenAffiliated withKrasnow Institute for Advanced Study, George Mason University Email author 
  • , Ross A. HammondAffiliated withCenter on Social Dynamics and Policy, The Brookings Institution

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George Kingsley Zipf observed in 1949 that the size distribution of cities within nations tends to follow a particular kind of power-law. This distribution is often described as the “rank size rule” or simply as the Zipf distribution. While Zipf convincingly documented this distribution, he was less successful in explaining its emergence. During the ensuing half century, various theories of city formation and development have emerged that have contributed real insights into the geography and economics of cities. For the most part, however, these theories have failed to predict the Zipf distribution of sizes. Another class of theories has been put forward to explain the distribution, but these have tended to rest on unrealistic assumptions, to lack explanatory power, or, at best, to lack the ability to explain the deviations from Zipf that can be observed in many nations. In this paper, we offer a simple agent-based model of city size evolution. This model offers substantial insight into the distribution of city sizes in various countries, while complementing previous work on the economic geography of cities and offering plausible economic interpretations and logic. The model can also account for several important categories of systematic deviation from Zipf that are observed in empirical data, and offers new insights about how such deviations arise.