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

02/18/2022
by   Robert Ganian, et al.
0

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).

READ FULL TEXT

page 1

page 2

page 3

page 4

11/20/2019

Individual-Based Stability in Hedonic Diversity Games

In hedonic diversity games (HDGs), recently introduced by Bredereck, Elk...
04/13/2018

Stable Outcomes in Modified Fractional Hedonic Games

In coalition formation games self-organized coalitions are created as a ...
11/11/2020

Mastermind with a Linear Number of Queries

Since the 60's Mastermind has been studied for the combinatorial and inf...
04/10/2018

Individual and Group Stability in Neutral Restrictions of Hedonic Games

We consider a class of coalition formation games called hedonic games, i...
11/03/2020

Hedonic Expertise Games

We consider a team formation setting where agents have varying levels of...
02/14/2022

Hedonic Games and Treewidth Revisited

We revisit the complexity of the well-studied notion of Additively Separ...