Stability of jurisdiction structures under the equal share and median rules

We consider a finite society with of individuals distributed along the real line. The individuals form jurisdictions to consume public projects, equally share their costs and, in addition, bear a transportation cost to the location of the project. We examine a core and Nash notions of stable jurisdiction structures and show that in hedonic games both solution sets could be empty. We demonstrate that in a quasi-hedonic set-up there is a Nash stable partition, but, in general, there are no core stable partitions. We then examine a subclass of societies that admits the existence of both types of stable partitions