Swap Stability in Schelling Games on Graphs

TL;DR

This paper explores swap Schelling games on graphs, analyzing the existence, complexity, and quality of stable configurations where agents swap positions to improve their neighborhood composition.

Contribution

It introduces and studies swap Schelling games, a novel variant allowing agents to swap positions, and analyzes their equilibrium properties and computational aspects.

Findings

Existence of equilibrium assignments under certain conditions

Complexity results for computing stable configurations

Insights into social welfare and diversity in equilibrium states

Abstract

We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple types; each agent either occupies a node of the graph and never moves away or aims to maximize the fraction of her neighbors who are of her own type. We consider a variant of this model that we call swap Schelling games, where the number of agents is equal to the number of nodes of the graph, and agents may {\em swap} positions with other agents to increase their utility. We study the existence, computational complexity and quality of equilibrium assignments in these games, both from a social welfare perspective and from a diversity perspective.