Individual and Group Stability in Neutral Restrictions of Hedonic Games

TL;DR

This paper explores stability concepts in hedonic games, introducing subset-neutral and neutrally anonymous classes, and proves the existence of stable partitions with algorithms for their computation.

Contribution

It defines subset-neutral and neutrally anonymous hedonic games, extending stability results and providing algorithms for stable partition existence.

Findings

Existence of Nash and individually stable partitions in subset-neutral hedonic games.

Neutrally anonymous hedonic games are a subclass of subset-additive hedonic games.

Algorithmic proof of a core stable and individually stable partition in neutrally anonymous games.

Abstract

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.