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The Schelling model of segregation was introduced in economics to show howmicro-motives can influence macro-behavior. Agents on a lattice have two colorsand try to move to a different location if the number of their neighbors with adifferent color exceeds some threshold. Simulations reveal that even such mildlocal color preferences, or homophily, are sufficient to cause segregation. Inthis work, we propose a stochastic generalization of the Schelling model, basedon both race and wealth, to understand how carefully architected placement ofincentives, such as urban infrastructure, might affect segregation. In ourmodel, each agent is assigned one of two colors along with a label, rich orpoor. Further, we designate certain vertices on the lattice as "urban sites,"providing civic infrastructure that most benefits the poorer population, thusincentivizing the occupation of such vertices by poor agents of either color.We look at the stationary distribution of a Markov process reflecting thesepreferences to understand the long-term effects. We prove that when incentivesare large enough, we will have "urbanization of poverty," an observed effectwhereby poor people tend to congregate on urban sites. Moreover, even whenhomophily preferences are very small, if the incentives are large and there isincome inequality in the two-color classes, we can get racial segregation onurban sites but integration on non-urban sites. In contrast, we find overallmitigation of segregation when the urban sites are distributed throughout thelattice and the incentives for urban sites exceed the homophily biases. Weprove that in this case, no matter how strong homophily preferences are, itwill be exponentially unlikely that a configuration chosen from stationaritywill have large, homogeneous clusters of agents of either color, suggesting wewill have racial integration with high probability.

A Heterogeneous Schelling Model for Wealth Disparity and its Effect on Segregation