The Third State of the Schelling Model of Residential Dynamics

TL;DR

This paper explores the complex dynamics of Schelling's segregation model, revealing a third persistent pattern beyond simple integration or segregation, influenced by agent behavior and group ratios.

Contribution

It introduces a third residential pattern in Schelling's model for unequal groups and emphasizes the importance of agent satisficing behavior for realistic outcomes.

Findings

Existence of a third persistent residential pattern for unequal groups.

Model dynamics depend on agents' satisficing behavior.

Traditional dichotomy of integration vs. segregation is incomplete.

Abstract

The Schelling model of segregation between two groups of residential agents (Schelling 1971; Schelling 1978) reflects the most abstract view of the non-economic forces of residential migrations: be close to people of 'your own'. The model assumes that the residential agent, located in the neighborhood where the fraction of 'friends' is less than a predefined threshold value F, tries to relocate to a neighborhood for which this fraction is above F. It is well known that for the equal groups, depending on F, Schelling's residential pattern converges either to complete integration (random pattern) or segregation. We investigate Schelling model pattern dynamics as dependent on F, the ratio of the group numbers and the size of the neighborhood and demonstrate that the traditional integrate-segregate dichotomy is incomplete. In case of unequal groups, there exists the wide interval of the F-values that entails the third persistent residential pattern, in which part of the majority population segregates, while the rest remains integrated with the minority. We also demonstrate that Schelling model dynamics essentially depends on the description of agents' residential behavior. To obtain sociologically meaningful results, the agents should be satisficers, and the fraction of the agents who relocate irrespective of the neighborhood state should be non-zero.