Combining Segregation and Integration: Schelling Model Dynamics for Heterogeneous Population

The Schelling model is a simple agent-based model that demonstrates how individuals' relocation decisions can 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 initially 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's steady patterns is richer than the segregation-integration dichotomy and contains patterns that consist of segregated patches of each of the two groups, alongside areas where both groups are spatially integrated. We obtain such patterns by considering a general version of the model in which the mechanisms of the agents' interactions remain the same, but the tolerance threshold varies between the agents of both groups. We show that the model produces patterns of mixed integration and segregation when the tolerance threshold of an essential fraction of agents is either low, below 1/5, or high, above 2/3. The emerging mixed patterns are relatively insensitive to the model's other parameters.