  In this paper we consider strategic cost sharing games with so-called
arbitrary sharing based on various combinatorial optimization problems, such as
vertex and set cover, facility location, and network design problems. We
concentrate on the existence and computational complexity of strong equilibria,
in which no coalition can improve the cost of each of its members. Our main
result reveals a connection between strong equilibrium in strategic games and
the core in traditional coalitional cost sharing games studied in economics.
For set cover and facility location games this results in a tight
characterization of the existence of strong equilibrium using the integrality
gap of suitable linear programming formulations. Furthermore, it allows to
derive all existing results for strong equilibria in network design cost
sharing games with arbitrary sharing via a unified approach. In addition, we
are able to show that in general the strong price of anarchy is always 1. This
should be contrasted with the price of anarchy of \Theta(n) for Nash
equilibria. Finally, we indicate that the LP-approach can also be used to
compute near-optimal and near-stable approximate strong equilibria.
