Strong equilibrium in cost sharing connection games

We study network games in which each player wishes to connect his source and sink, and the cost of each edge is shared among its users either equally (in Fair Connection Games—FCG's) or arbitrarily (in General Connection Games—GCG's). We study the existence and quality of strong equilibria (SE)—strategy profiles from which no coalition can improve the cost of each of its members—in these settings. We show that SE always exist in the following games: (1) Single source and sink FCG's and GCG's. (2) Single source multiple sinks FCG's and GCG's on series parallel graphs. (3) Multi source and sink FCG's on extension parallel graphs. As for the quality of the SE, in any FCG with n players, the cost of any SE is bounded by H(n) (i.e., the harmonic sum), contrasted with the Θ(n) price of anarchy. For any GCG, any SE is optimal.