# Hedonic Diversity Games: A Complexity Picture with More than Two Colors

arXiv: https://arxiv.org/abs/2202.09210 · HTML: https://mlsanity.com/paper/2202.09210/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2022.

## Built on by (most cited first, 4 of 4)

- [Strategic Resource Selection with Homophilic Agents](https://mlsanity.com/paper/2305.00843/) (2023)
- [Single-Peaked Jump Schelling Games](https://mlsanity.com/paper/2302.12107/) (2023)
- [Exact Algorithms and Lower Bounds for Forming Coalitions of Constrained Maximum Size](https://mlsanity.com/paper/2505.22384/) (2025)
- [The Complexity of Optimizing Atomic Congestion](https://mlsanity.com/paper/2312.10219/) (2023)

## Abstract (arXiv)

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 complete 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).