Individual and group stability in neutral restrictions of hedonic games

• We consider neutral restrictions of hedonic coalition formation games.
• Subset-additive hedonic games have the same representation power as hedonic games.
• A Nash stable partition and an individually stable partition exist in subset-neutral hedonic games.
• Neutrally anonymous hedonic games form a subclass of the subset-additive hedonic games.
• A core stable partition that is also individually stable exists in neutrally anonymous hedonic games.

We consider a class of coalition formation games called hedonic games, i.e., games in which the utility of a player is completely determined by the coalition that the player belongs to. We first define the class of subset-additive hedonic games and show that they have the same representation power as the class of hedonic games. We then define a restriction of subset-additive hedonic games that we call subset-neutral hedonic games and generalize a result by Bogomolnaia and Jackson (2002) by showing the existence of a Nash stable partition and an individually stable partition in such games. We also consider neutrally anonymous hedonic games and show that they form a subclass of the subset-additive hedonic games. Finally, we show the existence of a core stable partition that is also individually stable in neutrally anonymous hedonic games by exhibiting an algorithm to compute such a partition.