We study strategic games inspired by Schelling's seminal model of residential segregation. These games are played on undirected graphs, with the set of agents partitioned into multiple types; each agent either aims to maximize the fraction of her neighbors who are of her own type, or occupies a node of the graph and never moves away. We consider two natural variants of this model: in jump games agents can jump to empty nodes of the graph to increase their utility, while in swap games they can swap positions with other agents. We investigate the existence, computational complexity, and quality of equilibrium assignments in these games, both from a social welfare perspective and from a diversity perspective. Some of our results extend to a more general setting where the preferences of the agents over their neighbors are defined by a social network rather than a partition into types.

我们研究受谢林住宅隔离开创性模型启发的战略游戏。这些游戏是在无向图上进行的，代理集被划分为多种类型；每个代理要么旨在最大化她自己类型的邻居的比例，要么占据图中的一个节点并且永远不会离开。我们考虑这个模型的两个自然变体：在跳跃游戏中，代理可以跳转到图的空节点以增加它们的效用，而在交换游戏中，他们可以交换与其他代理的职位。我们从社会福利的角度和多样性的角度研究了这些游戏中均衡分配的存在性、计算复杂性和质量。我们的一些结果扩展到更一般的设置，其中代理对其邻居的偏好由社交网络定义，而不是由类型划分。