Strategic cooperation in cost sharing games

We examine strategic cost sharing games with so‐called arbitrary sharing based on various combinatorial optimization problems. These games have recently been popular in computer science to study cost sharing in the context of the Internet. We concentrate on the existence and computational complexity of strong equilibria (SE), in which no coalition can improve the cost of each of its members. Our main result reveals a connection to the core in coalitional cost sharing games studied in operations research. For set cover and facility location games this results in a tight characterization of the existence of SE using the integrality gap of suitable linear programming formulations. Furthermore, it allows to derive all existing results for SE in network design cost sharing games with arbitrary sharing via a unified approach. In addition, we show that in general there is no efficiency loss, i.e., the strong price of anarchy is always 1. Finally, we indicate how the LP‐approach is useful for the computation of near‐optimal and near‐stable approximate SE.