Absence-proofness: Group stability beyond the core
We introduce a new cooperative stability concept, absence-proofness (AP). Given a TU game (N,v), and a solution well defined for all subsocieties, a group of people S⊆N may benefit by partially seceding from cooperation. T⊆S stays out, and collects its stands alone benefits while S∖T receives its allocation specified by the solution at the reduced problem where only N∖T is present. We call a solution manipulable if S can improve upon its allocation in the original problem by such a maneuver, and solutions that are immune to such manipulations are called absence-proof. We show that population monotonicity (PM) implies AP, and AP implies separability. In minimum cost spanning tree problems, by replacing PM with AP, we propose a family of solutions that are easy to compute and more responsive than the well-known Folk solution to the asymmetries in the cost data, keeping all its fairness properties.