# Cooperative Dynamics of Neighborhood Economic Status in Cities

## TL;DR

This paper extends a city neighborhood model to include a potential function and wealth gain dynamics, successfully replicating observed patterns of economic status persistence and change across neighborhoods in American cities.

## Contribution

It introduces a novel model incorporating a neighborhood potential function, explaining long-term economic status patterns and their universality across cities.

## Key findings

- Larger fractions of rich and poor neighborhoods tend to retain status longer.
- The model replicates empirical patterns observed in American cities.
- Over time, middle-wealth and rich neighborhoods' status retention decreases significantly.

## 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.