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：近期，许多研究者受谢林住宅隔离模型的启发，对战略博弈进行了深入研究。在该模型中，属于$k$种不同类型的智能体被放置在网络的节点上。智能体可以是固执的，此时它们始终坚持选择自己偏好的位置；也可以是策略性的，此时它们旨在最大化其邻域中同类型智能体的比例。在受该模型启发而提出的所谓谢林博弈中，策略性智能体被视为寻求相似性：其效用定义为邻居中与其自身类型相同的比例。本文引入了一种新型的战略跳跃博弈，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其类型不同的比例。我们证明，当部分智能体固执时，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性，我们的寻求多样性跳跃博弈始终存在纯纳什均衡。在正则图、含单个空节点的蜘蛛图以及所有路径中，我们证明了更强的结论：该博弈为势博弈，即无论智能体初始位置如何，改进响应动态总是收敛至纳什均衡。