Hedonic Games

Aziz, Haris; Savani, Rahul; Moulin, Hervé

doi:10.1017/cbo9781107446984.016

Cited by 101 publications

(116 citation statements)

References 16 publications

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“…Fractional hedonic games, another natural and succinctly representable class of hedonic games by means of preference graphs, are introduced by Aziz et al (2014) from the cooperative perspective. They prove that the core can be empty for general graphs and that it is not empty in some classes of undirected unweighted graphs (that is, graphs with degree at most 2, multipartite complete graphs, bipartite graphs admitting a perfect matching and regular bipartite graphs).…”

Section: Related Workmentioning

confidence: 99%

“…In this work, we consider the class of (symmetric) fractional hedonic games introduced by Aziz, Brandt, and Harrenstein (2014). These games are modeled by an undirected graph in which nodes represent agents and edge weights the happiness of the corresponding endpoints for belonging to the same coalition.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, a seller wants to be situated in a group maximizing the number of buyers against the number of sellers, in order to be able to increase the price of the good and gain a higher profit. This scenario is referred to as Bakers and Millers (Aziz et al, 2014) and can be generalized to situations in which there are more than two types of agents by means of k-partite graphs.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

Bilò¹,

Fanelli²,

Flammini³

et al. 2018

jair

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We consider fractional hedonic games, a subclass of coalition formation games that can be succinctly modeled by means of a graph in which nodes represent agents and edge weights the degree of preference of the corresponding endpoints. The happiness or utility of an agent for being in a coalition is the average value she ascribes to its members. We adopt Nash stable outcomes as the target solution concept; that is we focus on states in which no agent can improve her utility by unilaterally changing her own group. We provide existence, efficiency and complexity results for games played on both general and specific graph topologies. As to the efficiency results, we mainly study the quality of the best Nash stable outcome and refer to the ratio between the social welfare of an optimal coalition structure and the one of such an equilibrium as to the price of stability. In this respect, we remark that a best Nash stable outcome has a natural meaning of stability, since it is the optimal solution among the ones which can be accepted by selfish agents. We provide upper and lower bounds on the price of stability for different topologies, both in case of weighted and unweighted edges. Beside the results for general graphs, we give refined bounds for various specific cases, such as triangle-free, bipartite graphs and tree graphs. For these families, we also show how to efficiently compute Nash stable outcomes with provable good social welfare.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation

Bilò¹,

Fanelli²,

Flammini³

et al. 2018

jair

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show abstract

“…It is immediate from Definition 9 that every instance of a-GASP has a non-empty core, and an outcome in the core can be constructed by a natural algorithm given below; we note that for hedonic games with dichotomous preferences, a similar algorithm has been proposed by Aziz et al (2016) (Proposition 8).…”

Section: Definitionmentioning

confidence: 99%

Group activity selection problem with approval preferences

et al. 2017

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We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents' preferences are binary, i.e., each agent classifies all pairs of the form '(activity, group size)' into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents' preferences satisfy certain natural constraints.

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“…However a wider class of matching problems, known as hedonic games, which include sr as a special case, are explored in Chapter 15 (Aziz and Savani, 2015).…”

Section: Concluding Remarks and Further Readingmentioning

confidence: 99%