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.

翻译：在大多数主要城市和都市区域，居民会按照种族或社会经济特征形成同质化社区。这一现象被称为居住隔离，已得到广泛研究。五十年前，谢林提出了一个具有里程碑意义的基于智能体的模型，以优雅的方式解释了居住隔离现象。近期一系列研究采用博弈论方法分析了谢林模型。然而，这些工作均考虑了给定数量离散类型（代表不同种族群体）的模型。我们聚焦于由非分类属性（如家庭收入或政治左-右光谱立场）导致的隔离问题。为此，我们考虑可用实数表示的主体类型。这为合理模型开辟了广阔的多样性空间，作为概念验证，我们重点研究了若干自然候选模型。具体而言，我们考虑了主体通过平均类型差异或最大类型差异来评价自身与邻居的差异，或通过设定对邻居类型值的特定容忍范围来评估其位置。我们研究了均衡的存在性与计算问题，并给出了无政府价格与稳定性的边界。此外，我们展示了模拟结果，以便比较各模型并揭示各变体所获均衡的特征。