Hedonic diversity games are a variant of the classical hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as colors in the model) and provided some initial complexity-theoretic and existential results concerning Nash and individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a comprehensive parameterized-complexity picture for computing Nash and individually stable outcomes with respect to the most natural parameterizations of the problem. Crucially, our results hold for general hedonic diversity games where the number of colors is not necessarily restricted to two, and show that—apart from two trivial cases—a necessary condition for tractability in this setting is that the number of colors is bounded by the parameter. Moreover, for the special case of two colors we resolve an open question asked in previous work (Boehmer and Elkind, AAAI 2020).

享乐多样性游戏是经典享乐游戏的变体，旨在更好地模拟有关多样性和公平性的各种问题。以前的工作主要针对具有两个多样性类别（在模型中表示为颜色）的情况，并提供了一些关于纳什和个体稳定结果的初始复杂性理论和存在主义结果。在这里，我们设计了带有下界的新算法，为计算纳什提供了全面的参数化复杂度图，并针对问题的最自然参数化提供了单独稳定的结果。至关重要的是，我们的结果适用于一般的享乐多样性游戏，其中颜色的数量不一定限于两种，并表明，除了两个微不足道的情况之外，在此设置中易处理的一个必要条件是颜色数量受参数限制。此外，对于两种颜色的特殊情况，我们解决了之前工作中提出的一个悬而未决的问题（Boehmer 和 Elkind，AAAI 2020）。