  This paper studies the Nash stability in hedonic coalition formation games.
We address the following issue: for a general problem formulation, is there any
utility allocation method ensuring a Nash-stable partition? We propose the
definition of the Nash-stable core. We study the conditions for having a
non-empty Nash-stable core. More precisely, we show how relaxed efficiency in
utility sharing method allows to ensure a non-empty Nash-stable core.

Computer Science and Game Theory