# Schelling Games on Graphs

## TL;DR

This paper studies a strategic game model inspired by Schelling's segregation model on graphs, analyzing equilibrium existence, computational complexity, and social welfare bounds, with extensions to social network preferences.

## Contribution

It introduces a new graph-based Schelling game model, analyzing equilibrium existence, complexity, and social welfare, including extensions to social network preferences.

## Key findings

- Existence results for equilibria in Schelling games on graphs.
- Complexity results for computing equilibria and high social welfare outcomes.
- Bounds on the price of anarchy and stability in these models.

## Abstract

We consider strategic games that are inspired by Schelling's model of residential segregation. In our model, the agents are partitioned into k types and need to select locations on an undirected graph. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. We investigate the existence of equilibria in these games, study the complexity of finding an equilibrium outcome or an outcome with high social welfare, and also provide upper and lower bounds on the price of anarchy and stability. Some of our results extend to the setting where the preferences of the agents over their neighbors are defined by a social network rather than a partition into types.