Existence of Stability in Hedonic Coalition Formation Games

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.