A physical analogue of the Schelling model (Alan Kirman and Dejan Vinkovic, 2006)

In a paper with Vinkovic (Kirman and Vinkovic 2006),

http://www.pnas.org/content/103/51/19261.full.pdf+html

Alan Kirman and his physicist co-author provide a mathematical link between Schelling’ssocio-economic model of segregation and the physics of clustering. More precisely, this paper shows the strong parallels between the structure of Schelling’s model and models used by physicists to study surface tension in liquids. Again, the paper reiterates one of the central lessons from Alan’s body of work: in order to understand how to go from the microeconomic level to a global behavior, we can and should borrow the insights of different disciplines. The final result is a richness of different metaphors, which, together, begin to form an orderly picture of an extraordinarily difficult problem. The fish market, the ants, the physics of surface tension, all contribute to our understanding of human interactions and their aggregate consequences.

The economic concept of ‘‘utility’’ is replaced by the physics concept of a particle’s internal energy. As a result cluster dynamics is driven by the ‘‘surface tension’’ force. The resultant segregated areas can be very large and can behave like spherical ‘‘liquid’’ droplets or as a collection of static clusters in ‘‘frozen’’ form. This model will hopefully provide a useful framework for studying many spatial economic phenomena that involve individuals making location choices as a function of the characteristics and choices of their neighbors.

Alan’s collaboration with physicists has been recurrent over the years, and the tools of
statistical physics in particular have been among Alan’s own favorite tools. Econophysics
models are represented in this issue by Weisbuch and Battiston’s paper. The paper studies a model where firms are connected through supply chains and investigates how local failures –(isolated failure to produce or deliver) can either spread to the system or give rise to localized concentrations of economic activity.

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