Combining segregation and integration: Schelling model dynamics for heterogeneous population

TL;DR

This paper extends the Schelling segregation model by allowing varying tolerance thresholds among agents, revealing a richer set of steady-state patterns that include both segregated and integrated patches, beyond the traditional dichotomy.

Contribution

It introduces a generalized Schelling model with heterogeneous tolerance thresholds, uncovering new mixed patterns of segregation and integration.

Findings

Mixed patterns occur when most agents' thresholds are below the tipping point or above 2/3.

The new patterns are relatively insensitive to model parameters in these regimes.

The model demonstrates a richer variety of steady states than previously recognized.

Abstract

The Schelling model is a simple agent based model that demonstrates how individuals' relocation decisions generate residential segregation in cities. Agents belong to one of two groups and occupy cells of rectangular space. Agents react to the fraction of agents of their own group within the neighborhood around their cell. Agents stay put when this fraction is above a given tolerance threshold but seek a new location if the fraction is below the threshold. The model is well known for its tipping point behavior: an initial random (integrated) pattern remains integrated when the tolerance threshold is below 1/3 but becomes segregated when the tolerance threshold is above 1/3. In this paper, we demonstrate that the variety of the Schelling model steady patterns is richer than the segregation-integration dichotomy and contains patterns that consist of segregated patches for each of the two groups alongside patches where both groups are spatially integrated. We obtain such patterns by considering a general version of the model in which the mechanisms of agents' interactions remain the same but the tolerance threshold varies between agents of both groups. We show that the model produces patterns of mixed integration and segregation when the tolerance threshold of most agents is either below the tipping point or above 2/3. In these cases, the mixed patterns are relatively insensitive to the model's parameters.