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Tipping Points in Schelling Segregation

One of the earliest agent-based economical models, Schelling's spacial proximity model illustrated how global segregation can emerge, often unwanted, from the actions of agents of two races acting in accordance with their individual local preferences. Here a 1-dimensional unperturbed variant of the model is studied, which is additionally open in the sense that agents may enter and exit the model. Following the authors' previous work in [1] and that of Brandt, Immorlica, Kamath, and Kleinberg in [2], rigorous results are established, whose statements are asymptotic in both the model and neighbourhood sizes. The current model's openness allows one race or the other to take over almost everywhere in a measure-theoretic sense. Tipping points are identified between the two regions of takeover and the region of staticity, in terms of the parameters of the model. In a significant generalization from previous work, the parameters comprise the initial proportions of the two races, along with independent values of the tolerance for each race.