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.

研究居住区划分如何受到非范畴属性的影响，并通过代理机制的多种模型，分析其平衡状态及稳定性，并进行了模拟结果比较。