# Schelling Games with Continuous Types

arXiv: https://arxiv.org/abs/2305.06819 · HTML: https://mlsanity.com/paper/2305.06819/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 36 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 8 of 8)

- [Schelling Segregation with Strategic Agents](https://mlsanity.com/paper/1806.08713/) (2018)
- [Schelling Games on Graphs](https://mlsanity.com/paper/1902.07937/) (2019)
- [Convergence and Hardness of Strategic Schelling Segregation](https://mlsanity.com/paper/1907.07513/) (2019)
- [Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games](https://mlsanity.com/paper/2204.12599/) (2022)
- [Topological Influence and Locality in Swap Schelling Games](https://mlsanity.com/paper/2005.02752/) (2020)
- [Modified Schelling Games](https://mlsanity.com/paper/2005.12149/) (2020)
- [Welfare Guarantees in Schelling Segregation](https://mlsanity.com/paper/2012.02086/) (2020)
- [Not all Strangers are the Same: The Impact of Tolerance in Schelling Games](https://mlsanity.com/paper/2105.02699/) (2021)

## Abstract (arXiv)

In most major cities and urban areas, residents form homogeneous neighborhoods along ethnic or socioeconomic lines. This phenomenon is widely known as residential segregation and has been studied extensively. Fifty years ago, Schelling proposed a landmark model that explains residential segregation in an elegant agent-based way. A recent stream of papers analyzed Schelling's model using game-theoretic approaches. However, all these works considered models with a given number of discrete types modeling different ethnic groups. We focus on segregation caused by non-categorical attributes, such as household income or position in a political left-right spectrum. For this, we consider agent types that can be represented as real numbers. This opens up a great variety of reasonable models and, as a proof of concept, we focus on several natural candidates. In particular, we consider agents that evaluate their location by the average type-difference or the maximum type-difference to their neighbors, or by having a certain tolerance range for type-values of neighboring agents. We study the existence and computation of equilibria and provide bounds on the Price of Anarchy and Stability. Also, we present simulation results that compare our models and shed light on the obtained equilibria for our variants.