Schelling segregation in an open city: A kinetically constrained Blume-Emery-Griffiths spin-1 system

Abstract

In the 70's Schelling introduced a multi-agent model to describe the segregation dynamics that may occur with individuals having only weak preferences for 'similar' neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city-lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a new variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socio-economic correlates.

Space Matters: Extending Sensitivity Analysis to Initial Spatial Conditions in Geosimulation Models

“…They reveal conjoint and non-linear effects on the vacancy rates and tolerance levels on segregation patterns. Gauvin et al (2010) run Schelling's segregation process in an open city-lattice to study how the variations in tolerance levels, vacancy rates and city attractiveness may create lines of vacancy lots between clusters of agents. They conclude on the functional role of vacancies, which allow weakly tolerant agents to live and be satisfied in a city environment they nevertheless perceive as hostile.…”

Group formation through indirect reciprocity

“…Group formation in human society has attracted much interest in statistical physics as a example of self-organizing phenomena in complex systems [1][2][3][4]. Social systems include complex interactions which are unconventional in physics.…”

A unified framework for Schelling’s model of segregation

“…For example, we see that moving from randomly jumping agents which are popular in the physics literature [11,18,19] to best-response dynamics favoured by economists [7,8] does not result in a qualitative change to the way in which segregation develops. Simulation results for the time evolution of interface density in five different models taken from several disciplines were presented, each displaying the same characteristic form in short to medium timescales.…”

“…Schelling himself produced several iterations of his first model [1,2,3]; a consequence of which is that there is no definitive "Schelling model". As computing power increased many researchers have simulated model variants related to their particular interests [4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21], finding segregation everywhere from the suburbs of Tel-Aviv [15] to the Sierpinski fractal [20].…”

“…In particular, publications in the physics literature have gone to some considerable efforts to map the Schelling model onto systems already known to them, including liquids [22] and spin models [6,17,18,19]. Whilst such analogies are interesting, they imply that the models ought to be studied from a within particular physical formalism, even though the corresponding assumptions, techniques and results may not necessarily be the most relevant to the interests of researchers in other fields.…”