Topological Influence and Locality in Swap Schelling Games

TL;DR

This paper explores how the underlying topology and local swap restrictions affect the existence of equilibria, efficiency, and dynamics in strategic Schelling segregation models on various graph structures.

Contribution

It provides new bounds on the Price of Anarchy and analyzes the impact of locality restrictions on game dynamics in topological segregation models.

Findings

Improved bounds on Price of Anarchy for arbitrary graphs.

Almost tight bounds for regular graphs, paths, and cycles.

Locality restrictions significantly affect game dynamics on grids.

Abstract

Residential segregation is a wide-spread phenomenon that can be observed in almost every major city. In these urban areas residents with different racial or socioeconomic background tend to form homogeneous clusters. Schelling's famous agent-based model for residential segregation explains how such 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. Very recently, Schelling's model has been investigated from a game-theoretic point of view with selfish agents that strategically select their residential location. In these games, agents can improve on their current location by performing a location swap with another agent who is willing to swap. We significantly deepen these investigations by studying the influence of the underlying topology modeling the residential area on the existence of equilibria, the Price of Anarchy and on the dynamic properties of the resulting strategic multi-agent system. Moreover, as a new conceptual contribution, we also consider the influence of locality, i.e., if the location swaps are restricted to swaps of neighboring agents. We give improved almost tight bounds on the Price of Anarchy for arbitrary underlying graphs and we present (almost) tight bounds for regular graphs, paths and cycles. Moreover, we give almost tight bounds for grids, which are commonly used in empirical studies. For grids we also show that locality has a severe impact on the game dynamics.