Residential segregation is a widespread phenomenon that can be observed in almost every major city. In these urban areas, residents with different ethnical or socioeconomic backgrounds tend to form homogeneous clusters. In Schelling’s classical segregation model two types of agents are placed on a grid. An agent is content with its location if the fraction of its neighbors, which have the same
type as the agent, is at least g, for some 0 ≤ τ ≤ 1. Discontent agents simply swap their location with a randomly chosen other discontent agent or jump to a random empty location. The model gives a coherent explanation of how clusters can form even if all agents are tolerant, i.e., if they agree to live in mixed neighborhoods. For segregation to occur, all it needs is a slight bias towards agents preferring similar neighbors.
Although the model is well studied, previous research focused on a random process point of view. However, it is more realistic to assume instead that the agents strategically choose where to live. We close this gap by introducing and analyzing game-theoretic models of Schelling segregation, where rational agents strategically choose their locations.
As the the first step, we introduce and analyze a generalized game-theoretic model that allows more than two agent types and more general underlying graphs modeling the residential area. We introduce different versions of Swap and Jump Schelling Games. Swap Schelling Games assume that every vertex of the underlying graph serving as a residential area is occupied by an agent and pairs of discontent agents can swap their locations, i.e., their occupied vertices, to increase their utility. In contrast, for the Jump Schelling Game, we assume that there exist empty vertices in the graph and agents can jump to these vacant vertices if this increases their utility. We show that the number of agent types as well as the structure of underlying graph heavily influence the dynamic properties and the tractability of finding an optimal strategy profile.
As a second step, we significantly deepen these investigations for the swap version with τ = 1 by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy, and the dynamic properties. Moreover, we restrict the movement of agents locally. As a main takeaway, we find that both aspects influence the existence and the quality of stable states.
Furthermore, also for the swap model, we follow sociological surveys and study, asking the same core game-theoretic questions, non-monotone single-peaked utility functions instead of monotone ones, i.e., utility functions that are not monotone in the fraction of same-type neighbors. Our results clearly show that moving from monotone to non-monotone utilities yields novel structural properties and different results in terms of existence and quality of stable states. In the last part, we introduce an agent-based saturated open-city variant, the Flip Schelling Process, in which agents, based on the predominant type in their neighborhood, decide whether to change their types. We provide a general framework for analyzing the influence of the underlying topology on residential segregation and investigate the probability that an edge is monochrome, i.e., that both incident vertices have the same type, on random geometric and Erdös–Rényi graphs. For random geometric graphs, we prove the existence of a constant c > 0 such that the expected fraction of monochrome edges after the Flip Schelling Process is at least ½+c. For Erdös–Rényi graphs, we show the expected fraction of monochrome edges after the Flip Schelling Process is at most ½ + o(1).
