Bridging the divide: Economic exchange and segregation in dual-income cities

Abstract

Segregation is a growing concern around the world. One of its main manifestations is the creation of ghettos, whose inhabitants have difficult access to well-paid jobs, which are often located far from their homes. In order to study this phenomenon, we propose an extension of Schelling's model of segregation to take into account the existence of economic exchanges. To approximate a geographical model of the city, we consider a small-world network with a defined real estate market. The evolution of the system has also been studied, finding that economic exchanges follow exponential laws and relocations are approximated by power laws. In addition to this, we consider the existence of delays in the actions of the agents, which mainly affect the happiness of those with fewer economic resources. Besides, the size of the economic exchange plays a crucial role in overall segregation. Despite its simplicity, we find that our model reproduces real-world situations such as the separation between favoured and handicapped economic areas, the importance of economic contacts between them to improve the distribution of wealth, and the existence of efficient and cheap transport to break the poverty cycles typical of disadvantaged zones.

Figures (7)

• Figure 1: Small-world network of $50$ nodes with $6$ nearest neighbors and a rewiring prpbability of $0.1$. Two possible values of housing expenses are illustrated via node shapes. Node degrees are associated to the color scheme. The represented network will be considered fixed unless otherwise stated.
• Figure 2: Circular graph where each sector corresponds to the node in the system from Fig. \ref{['Fig:sw']}. $\bar{S_i}$, $\bar{O_i}$ and $\bar{H_i}$ denote the the mean spin, occupation and happiness in the $i$ node.
• Figure 3: (a) Economic exchange matrix $\textbf{T}$ in $q$ monetary units. Positive values indicate that the node acts as a monetary sink, while negative values indicate sources. The matrix is antisymmetric, given that when one agent gives a quantity $q$, $-1$ for the agent, the other receives it, $+1$. (b) Chord diagram of economic exchanges exceeding $|T_{ij}| \geq 1.5$, where $i$ and $j$ are node numbers. The value was chosen to preserve the principal net economic transfers between regions, see (a) scale. The external number indicates the mean number of exchanges.
• Figure 4: Evolution of the number of economic exchanges (a) and relocations (b). Time is measured in Monte-Carlo (MC) steps. Each step involves a relocation or economic exchange attempt of all the unsatisfied agents in the system. Measures are averaged over 10,000 system runs.
• Figure 5: (a) Economic exchanges evolution in Monte-Carlo steps for different economic exchange sizes $q$. (b) Mean agent happiness (grey) and Integration (gold) versus $q$.