Segregation in Social Networks

In a series of papers, Schelling presented a microeconomic model of neighbourhood segregation that he called a "spatial proximity model". The model specifies a spatial setup in which the individual agents care only about the composition of their own local neighbourhood. Agents belong to two types and are placed on regular (one- or two-dimensional) lattices and hold Moore-types of neighborhoods. The idea that people care about their spatial proximity has been justified by the observation that this is where people mow the lawn, where their children play outside, where people do their shopping, and park their car. However, people also interact through networks of friends, relatives, and colleagues, and through virtual communities on the internet. Segregation may not necessarily occur at the spatial (neighbourhood) level only. More generally, one might conceive groups of people who are socially segregated despite being spatially integrated. In this paper, then, we extend Schelling's analysis by analyzing segregation in a range of network structures (random, regular, small-world, scale-free, etc.). We stick to Schelling’s original formulation as far as agents, preferences, and choices are concerned. More specifically, we consider a population of N agents, randomly placed on the nodes of a undirected graph. We leave a certain percentage of the graph nodes empty. Hence, the neighbourhood of each agent is defined by the other directly linked nodes. Agents are of two types (say, A and B) and hold standard Schelling-type preferences (i.e. an agent is unhappy if more than 50% of his neighbours are different, and is happy otherwise). We analyze best-response dynamics in two setups. In the first setup, we assume that networks are exogenously fixed through time. The main question is whether the mild preferences entailed by Schelling’s formulation, combined with best-response dynamics, can explain segregation also in such more general networks. We begin with an exploration of the class of k-degree regular networks (i.e. graphs where all agents hold exactly k links). We then explore the consequences of assuming (i) random networks (where each link with any two agents is present with a probability 0