Existence of Stability in Hedonic Coalition Formation Games

TL;DR

This paper investigates conditions under which stable partitions exist in hedonic coalition formation games, focusing on preference restrictions like top and bottom responsiveness, with implications for additive and B-preference subclasses.

Contribution

It establishes the existence of stable partitions under specific preference restrictions, extending understanding of stability in hedonic games with natural subclasses.

Findings

Stable partitions exist under top and bottom responsiveness.

Existence results apply to additive and B-preference subclasses.

Stronger stability concepts do not guarantee existence.

Abstract

In this paper, we examine \emph{hedonic coalition formation games} in which each player's preferences over partitions of players depend only on the members of his coalition. We present three main results in which restrictions on the preferences of the players guarantee the existence of stable partitions for various notions of stability. The preference restrictions pertain to \emph{top responsiveness} and \emph{bottom responsiveness} which model optimistic and pessimistic behavior of players respectively. The existence results apply to natural subclasses of \emph{additive separable hedonic games} and \emph{hedonic games with \B-preferences}. It is also shown that our existence results cannot be strengthened to the case of stronger known stability concepts.