The Stability of Hedonic Coalition Structures

Bogomolnaia, Anna; Jackson, Matthew O.

doi:10.1006/game.2001.0877

Cited by 662 publications

(768 citation statements)

References 15 publications

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“…The main difference between anonymous hedonic games and our problem is that, in our setting, the agents' preferences depend not only on the group size, but also on the activity that has been allocated to their group; thus, our model can be seen as a generalization of anonymous hedonic games. We remark that we can represent our problem as a general (i.e., nonanonymous) hedonic game (Banerjee et al 2001;Bogomolnaia and Jackson 2002), by creating a dummy agent for each activity and endowing it with suitable preferences (see Sect. 2.2 for details).…”

Section: Related Workmentioning

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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Section: Related Workmentioning

confidence: 99%

Group activity selection problem with approval preferences

et al. 2017

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“…The purpose of this brief note is to place the game-theoretical interpretation of Gamson's law in the context of hedonic games developed by Banerjee, Konishi and S• onmez (2001) (BKS -henceforth) (see also Bogomolnaia and Jackson (2002)). In this framework the payo of every player payo depends only on the composition of the coalition she belongs to.…”

Section: Motivationmentioning

confidence: 99%

“…This note adds one celebrated coalition formation game due to Gamson (1961) in the list of applications of the theory of hedonic games explored by Banerjee, Konishi and S• omnez (2001) and Bogomolnaia and Jackson (2002). We apply their results to study the original Gamson game and o er extensions both to a multi-dimensional characteristics space and to an in nite number of players.…”

Section: Introductionmentioning

confidence: 99%

“…

AbstractThis note adds one celebrated coalition formation game due to Gamson (1961) in the list of applications of the theory of hedonic games explored by Banerjee, Konishi and S• omnez (2001) and Bogomolnaia and Jackson (2002). We apply their results to study the original Gamson game and o er extensions both to a multi-dimensional characteristics space and to an in nite number of players.

JEL Classi cation Numbers: C71, D71, Z1.

Keywords: Gamson's law, hedonic games, coalition formation, winning coalitions.

We thank an anonymous referee for insightful comments and suggestions on the previous version of this note.

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confidence: 99%

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Gamson’s law and hedonic games

2007

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This note adds one celebrated coalition formation game due to Gamson (1961) in the list of applications of the theory of hedonic games explored by Banerjee, Konishi and S• omnez (2001) and Bogomolnaia and Jackson (2002). We apply their results to study the original Gamson game and o er extensions both to a multi-dimensional characteristics space and to an in nite number of players. JEL Classi cation Numbers: C71, D71, Z1.Keywords: Gamson's law, hedonic games, coalition formation, winning coalitions.We thank an anonymous referee for insightful comments and suggestions on the previous version of this note.

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“…In general, coalition structures in the core of the coalition formation game would be great candidates for a solution (though not necessarily the only ones). But since the core is empty unless one imposes strong assumptions on the domain of games (see Banerjee, Konishi, andSönmez, 2001, andBogomolnaia andJackson, 2002), it has rather limited predictive power. For our example, the only possibilities left by the preceding axioms were to either identify three stable coalition structures or none.…”

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confidence: 99%