Agent-Based Modelling - GeoComputation - page 216

9.3 EXAMPLE OF EXPLORATORY AB MODELLING: SCHELLING
MODEL OF ETHNIC RESIDENTIAL DYNAMICS
The objective of the Schelling model is to explain ethnic segregation in a city. The model population
consists of two ethnic groups of householders (householder agents), whose members seek residence
in a city of one-family dwellings represented by the cells of a rectangular grid. Householders pre-
fer residing within neighbourhoods of similar ethnic makeup, where the fraction of the members
of their group, referred to by Schelling (1971) as friends , is sufficiently high and a householder is
happy . Formally, this means that the fraction f of friends within the neighbourhood around the
agent's location is above a certain threshold value F, f > F. The traditional approach is to consider F
as a control parameter and investigate the model dynamics as depending upon F.
Well-known results from previous model studies are as follows: there exists a critical value
of F = F crit such that when F < F crit , the spatial distribution of the members of the two groups will
become random over time, regardless of the initial distribution in the city; an example is shown in
Figure 9.5a. When F ≥ F crit , the agents' residential pattern converges, in time, to segregation irre-
spective of the initial pattern, as shown in Figure 9.5b. The value of F crit varies between 0.25 and
0.30, depending upon the model details.

9.3.1 a gentS , o BjectS and r elationShiPS
The set of entities in the Schelling model consists of cells , that is, one-family dwellings, and house-
holder agents . Cell objects have no properties other than their location, while householder agents
have Boolean ethnicity . The location and neighbourhoods of the agents in the Schelling model are
defined using relationships. The latter makes it possible to develop a Schelling model irrespective of
the partitioning of space into dwellings (Figure 9.6).

9.3.2 B ehaVioural r uleS
The way in which a Schelling agent makes residential decisions can be implemented in several
ways although it is not possible to provide all the details here. An agent has to decide if it wants to
reside, if there are vacant locations to reside in, if one or more of these locations are good enough
to move to and, if so, which of them to choose. The student of the Schelling model has to decide on
the following:

(a) (b)

FIGURE 9.5 Persistent residential patterns of the Schelling model for two equal groups, where the total
density of agents is 98%: (a) F = 0.2, random pattern; (b) F = 0.8, segregated pattern. (From Benenson, I. and
Hatna, E., Geogr. Anal. , 43, 287, 2011.)