Pareto Optimal Coalitions of Fixed Size

Cseh, Ágnes; Fleiner, Tamás; Harján, Petra

doi:10.22574/jmid.2019.11.003

Cited by 7 publications

(6 citation statements)

References 20 publications

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“…(Peters 2016) studies the computational complexity of questions related to finding optimal and several stable partitions (swap stability is not considered) for the roommate problem with dichotomous preferences. Finally, (Cseh, Fleiner, and Harján 2019) consider the problem of partitioning agents into groups of fixed size and study the complexity of deciding the existence of, and then finding, a Pareto optimal assignment, and the complexity of verifying Pareto optimality for a given assignment.…”

Section: Related Workmentioning

confidence: 99%

Hedonic Games with Fixed-Size Coalitions

Bilò

Monaco

Moscardelli

2022

AAAI

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In hedonic games, a set of n agents, having preferences over all possible coalition structures, needs to agree on a stable outcome. In this work, we initiate the study of hedonic games with fixed-size coalitions, where the set of possible coalition structures is restricted as follows: there are k coalitions, each coalition has a fixed size, and the sum of the sizes of all coalitions equals n. We focus on the basic model of additively separable hedonic games with symmetric preferences, where an agent's preference is captured by a utility function which sums up a contribution due to any other agent in the same coalition. In this setting, an outcome is stable if no pair of agents can exchange coalitions and improve their utilities. Conditioned on the definition of improvement, three stability notions arise: swap stability under transferable utilities, which requires to improve the sum of the utilities of both agents, swap stability, which requires to improve the utility of one agent without decreasing the utility of the other one, and strict swap stability, requiring to improve the utilities of both agents simultaneously. We analyse the fundamental questions of existence, complexity and efficiency of stable outcomes, and that of complexity of a social optimum.

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Section: Related Workmentioning

confidence: 99%

Hedonic Games with Fixed-Size Coalitions

Bilò

Monaco

Moscardelli

2022

AAAI

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“…Considering the sublist ML ′ i arising from ML i by deleting all 2-sets containing an agent x k i , one sees that the first 15 sets of two agents of this sublist only consider agents of z k,p i for p ∈ [6], and all agents z k,p i are matched to one of these 15 sets of size two. Thus, any blocking 2-set containing an agents z k,p i consists only of agents from {z k,q i : q ∈ [6]}.…”

Section: Proof Of Claimmentioning

confidence: 99%

“…treewidth (MSO-based) [16,30]. Other research considers hedonic games with fixed coalition size [6], but aims for Pareto optimal outcomes instead of core stability which we consider.…”

Section: Introductionmentioning

confidence: 99%

Multidimensional Stable Roommates with Master List

Bredereck¹,

Heeger²,

Knop³

et al. 2020

Preprint

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Since the early days of research in algorithms and complexity, the computation of stable matchings is a core topic. While in the classic setting the goal is to match up two agents (either from different "gender" (this is Stable Marriage) or "unrestricted" (this is Stable Roommates)), Knuth [1976] triggered the study of three-or multidimensional cases.Here, we focus on the study of Multidimensional Stable Roommates, known to be NP-hard since the early 1990's. Many NP-hardness results, however, rely on very general input instances that do not occur in at least some of the specific application scenarios. With the quest for identifying islands of tractability, we look at the case of master lists. Here, as natural in applications where agents express their preferences based on "objective" scores, one roughly speaking assumes that all agent preferences are "derived from" a central master list, implying that the individual agent preferences shall be similar. Master lists have been frequently studied in the two-dimensional (classic) stable matching case, but seemingly almost never for the multidimensional case. This work, also relying on methods from parameterized algorithm design and complexity analysis, performs a first systematic study of Multidimensional Stable Roommates under the assumption of master lists.

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“…Other research involving hedonic games with similar constraints has considered Pareto optimality rather than stability [13]; 'flatmate games', in which any coalition contains three or fewer agents [9]; and strategic aspects [27].…”

Section: Introductionmentioning

confidence: 99%

The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

McKay

Manlove

2021

Lecture Notes in Computer Science

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The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A number of three-dimensional variants exist, in which agents are instead matched into triples. Both the original problem and these variants can also be viewed as hedonic games. We formalise a three-dimensional variant using general additively separable preferences, in which each agent provides an integer valuation of every other agent. In this variant, we show that a stable matching may not exist and that the related decision problem is NP-complete, even when the valuations are binary. In contrast, we show that if the valuations are binary and symmetric then a stable matching must exist and can be found in polynomial time. We also consider the related problem of finding a stable matching with maximum utilitarian welfare when valuations are binary and symmetric. We show that this optimisation problem is NPhard and present a novel 2-approximation algorithm.

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Pareto Optimal Coalitions of Fixed Size

Cited by 7 publications

References 20 publications

Hedonic Games with Fixed-Size Coalitions

Hedonic Games with Fixed-Size Coalitions

Multidimensional Stable Roommates with Master List

The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

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