Recently, many researchers have studied strategic games inspired by Schelling's influential model of residential segregation. In this model, agents belonging to $k$ different types are placed at the nodes of a network. 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. In the so-called Schelling games inspired by this model, strategic agents are assumed to be similarity-seeking: their utility is defined as the fraction of its neighbors of the same type as itself. In this paper, we introduce a new type of strategic jump game in which agents are instead diversity-seeking: the utility of an agent is defined as the fraction of its neighbors that is of a different type than itself. We show that it is NP-hard to determine the existence of an equilibrium in such games, if some agents are stubborn. However, in trees, our diversity-seeking jump game always admits a pure Nash equilibrium, if all agents are strategic. In regular graphs and spider graphs with a single empty node, as well as in all paths, we prove a stronger result: the game is a potential game, that is, improving response dynamics will always converge to a Nash equilibrium from any initial placement of agents.

翻译：最近，许多学者研究了受Schelling经典居住隔离模型启发的策略博弈。在该模型中，属于$k$种不同类型的智能体被放置于网络的节点上。智能体可能是固执型的——此时它们总会选择自己偏好的位置；也可能是策略型的——此时它们的目标是最大化自身邻域中同类型智能体的比例。在受此模型启发的所谓Schelling博弈中，策略型智能体被假定为寻求相似：其效用定义为邻居中与自己同类型的比例。本文提出一种新型策略跳跃博弈，其中智能体转而寻求多样性：智能体的效用定义为邻居中与自己不同类型的比例。我们证明，当存在固执型智能体时，判断此类博弈是否存在均衡是NP难的。然而，在树形结构中，若所有智能体均为策略型，则我们的面向多样性的跳跃博弈始终存在纯纳什均衡。对于正则图、含单一空节点的蛛网图以及所有路径图，我们证明了一个更强的结论：该博弈是一个势博弈，即从任何初始智能体布局出发，改进响应动态总会收敛到纳什均衡。