Abstract
We significantly extend our earlier variant of the Schelling model, incorporating a neighborhood Potential function as well as an agent wealth gain function to study the long term evolution of the economic status of neighborhoods in cities. We find that the long term patterns of neighborhood relative economic status (RES) simulated by this model reasonably replicate the empirically observed patterns from American cities. Specifically, we find that larger fractions of rich and poor neighborhoods tend to, on average, retain status for longer than lower- and upper-middle wealth neighborhoods. The use of a Potential function that measures the relative wealth of neighborhoods as the basis for agent wealth gain and agent movement appears critical to explaining these emergent patterns of neighborhood RES. This also suggests that the empirically observed RES patterns could indeed be universal and that we would expect to see these patterns repeated for cities around the world. Observing RES behavior over even longer periods of time, the model predicts that the fraction of poor neighborhoods retaining status remains almost constant over extended periods of time, while the fraction of middle-wealth and rich neighborhoods retaining status reduces significantly over time, tending to zero.
Highlights
Cities are increasingly being seen as systems that are potentially amenable to exploration through the tools of complex systems science and statistical physics
If wealth of the agent (Wa) ! wealth of the randomly selected receiving site (WRMed), the agent moves with probability, pmove = 1. (Previously [16], we described in detail this inversion of the classic Schelling model [1] by replacing the tolerance level (τ) of an agent with a threshold level (T) presented to all agents by extant neighborhood wealth configurations.) If not, the move occurs stochastically with probability pmove (Eq 3): pmove 1⁄4 exp ðbmoveðWa À WRMedÞÞ
While the only decision an agent made in the previous model was whether to move, based on a simple of comparison of the median wealths of her current neighborhood and a randomly chosen alternate neighborhood, our current model describes a richer phenomenology incorporating the dynamics of agent choice, agent movement, and agent wealth gain
Summary
Cities are increasingly being seen as systems that are potentially amenable to exploration through the tools of complex systems science and statistical physics. This includes work on processes underlying the the emergence of inequitous outcomes such as segregation. The Schelling model [1] explained the emergence of racial segregation in terms of interactions of individual preferences, with even small preferences for like neighbors at an individual level leading to emergent segregated patterns at a collective level. The tools of statistical mechanics have been used to study the underlying phase transition
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