Absence-proofness: Group stability beyond the core

We introduce a new cooperative stability concept, absence-proofness (AP). Given a TU game , and a solution well defined for all subsocieties, a group of people may benefit by partially seceding from cooperation. stays out, and collects its stands alone benefits while receives its allocation specified by the solution at the reduced problem where only is present. We call a solution manipulable if 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.