Stable outcomes in modified fractional hedonic games

Monaco, Gianpiero; Moscardelli, Luca; Velaj, Yllka

doi:10.1007/s10458-019-09431-z

Cited by 20 publications

(12 citation statements)

References 41 publications

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“…In order to get the equivalence among the two games, the hedonic utility of an agent v can be defined as the overall number of its neighbors minus the number of agents of its neighborhood that are in the same coalition. Nash equilibria issues in hedonic games have been largely investigated under several different assumptions [5,6,20] (just to cite a few).…”

Section: Introductionmentioning

confidence: 99%

Coalition Resilient Outcomes in Max k-Cut Games

Carosi

Fioravanti

Gualà

et al. 2019

Lecture Notes in Computer Science

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We investigate strong Nash equilibria in the max k-cut game, where we are given an undirected edge-weighted graph together with a set {1, . . . , k} of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player v consists of the k colors. When players select a color they induce a k-coloring or simply a coloring. Given a coloring, the utility (or payoff ) of a player u is the sum of the weights of the edges {u, v} incident to u, such that the color chosen by u is different from the one chosen by v. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish agents and extend or are related to several fundamental classes of games. Very little is known about the existence of strong equilibria in max k-cut games. In this paper we make some steps forward in the comprehension of it. We first show that improving deviations performed by minimal coalitions can cycle, and thus answering negatively the open problem proposed in [13]. Next, we turn our attention to unweighted graphs. We first show that any optimal coloring is a 5-SE in this case. Then, we introduce x-local strong equilibria, namely colorings that are resilient to deviations by coalitions such that the maximum distance between every pair of nodes in the coalition is at most x. We prove that 1-local strong equilibria always exist. Finally, we show the existence of strong Nash equilibria in several interesting specific scenarios.

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Section: Introductionmentioning

confidence: 99%

Coalition Resilient Outcomes in Max k-Cut Games

Carosi

Fioravanti

Gualà

et al. 2019

Lecture Notes in Computer Science

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“…Olsen (2012) considers a variant of FHGs called modified fractional hedonic games, where the utility of each agent in a coalition structure is equal to the sum of the weights of the incident edges in the coalition she belongs to, divided by the size of the coalition minus 1. Monaco, Moscardelli, and Velaj (2020) consider Nash and core stable outcomes for modified fractional hedonic games and provide bounds on their performance. Finally, Bullinger (2020) gives algorithms for finding Pareto optimal solutions in ASHGs, FHGs and modified FHGs.…”

Section: Related Workmentioning

confidence: 99%

Strategyproof Mechanisms for Additively Separable and Fractional Hedonic Games

Flammini

Kodric

Monaco

et al. 2021

jair

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Additively separable hedonic games and fractional hedonic games have received considerable attention in the literature. They are coalition formation games among selfish agents based on their mutual preferences. Most of the work in the literature characterizes the existence and structure of stable outcomes (i.e., partitions into coalitions) assuming that preferences are given. However, there is little discussion of this assumption. In fact, agents receive different utilities if they belong to different coalitions, and thus it is natural for them to declare their preferences strategically in order to maximize their benefit. In this paper we consider strategyproof mechanisms for additively separable hedonic games and fractional hedonic games, that is, partitioning methods without payments such that utility maximizing agents have no incentive to lie about their true preferences. We focus on social welfare maximization and provide several lower and upper bounds on the performance achievable by strategyproof mechanisms for general and specific additive functions. In most of the cases we provide tight or asymptotically tight results. All our mechanisms are simple and can be run in polynomial time. Moreover, all the lower bounds are unconditional, that is, they do not rely on any computational complexity assumptions.

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“…Another relevant class of hedonic games is that of fractional hedonic games, studied in (Aziz et al 2019;Peters and Elkind 2015;Olsen 2012;Monaco, Moscardelli, and Velaj 2018;Carosi, Monaco, and Moscardelli 2019;Bilò et al 2018;Flammini et al 2018;Monaco, Moscardelli, and Velaj 2019). The inefficiency of these and other related classes of hedonic games under different stability and optimality notions has been considered in (Elkind, Fanelli, and Flammini 2016;Balliu et al 2019;Balliu, Flammini, and Olivetti 2017;Flammini, Monaco, and Zhang 2017).…”

Section: Related Workmentioning

confidence: 99%

The Impact of Selfishness in Hypergraph Hedonic Games

Aloisio

Flammini

Vinci

2020

AAAI

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We consider a class of coalition formation games that can be succinctly represented by means of hypergraphs and properly generalizes symmetric additively separable hedonic games. More precisely, an instance of hypegraph hedonic game consists of a weighted hypergraph, in which each agent is associated to a distinct node and her utility for being in a given coalition is equal to the sum of the weights of all the hyperedges included in the coalition. We study the performance of stable outcomes in such games, investigating the degradation of their social welfare under two different metrics, the k-Nash price of anarchy and k-core price of anarchy, where k is the maximum size of a deviating coalition. Such prices are defined as the worst-case ratio between the optimal social welfare and the social welfare obtained when the agents reach an outcome satisfying the respective stability criteria. We provide asymptotically tight upper and lower bounds on the values of these metrics for several classes of hypergraph hedonic games, parametrized according to the integer k, the hypergraph arity r and the number of agents n. Furthermore, we show that the problem of computing the exact value of such prices for a given instance is computationally hard, even in case of non-negative hyperedge weights.

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Stable outcomes in modified fractional hedonic games

Cited by 20 publications

References 41 publications

Coalition Resilient Outcomes in Max k-Cut Games

Coalition Resilient Outcomes in Max k-Cut Games

Strategyproof Mechanisms for Additively Separable and Fractional Hedonic Games

The Impact of Selfishness in Hypergraph Hedonic Games

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