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

Fuente: arXiv
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Autori principali: Ganian, Robert, Hamm, Thekla, Knop, Dušan, Schierreich, Šimon, Suchý, Ondřej
Natura: Preprint
Pubblicazione: 2022
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author Ganian, Robert
Hamm, Thekla
Knop, Dušan
Schierreich, Šimon
Suchý, Ondřej
author_facet Ganian, Robert
Hamm, Thekla
Knop, Dušan
Schierreich, Šimon
Suchý, Ondřej
contents 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).
format Preprint
id arxiv_https___arxiv_org_abs_2202_09210
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Hedonic Diversity Games: A Complexity Picture with More than Two Colors
Ganian, Robert
Hamm, Thekla
Knop, Dušan
Schierreich, Šimon
Suchý, Ondřej
Computer Science and Game Theory
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).
title Hedonic Diversity Games: A Complexity Picture with More than Two Colors
topic Computer Science and Game Theory
url https://arxiv.org/abs/2202.09210