A fundamental network design problem is the one of Steiner Network Design. The goal is to design a network which is able to support a unit flow for each commodity, at a time, between its source-sink pair. When the flows are unsplittable, this corresponds to the Steiner forest problem and to the problem of sharing cost of the multicast by different users. As a result of greedy selfish behavior of users in the network design game, the overall quality of the resulting solution is often not as good as the globally optimum solution of the underlying problem. We are therefore interested in the problem of designing distributed cost sharing mechanisms that induce the selfish agents to converge to the near-optimum solutions. Our main contribution is showing that 1+epsilon ratio can be achieved by (non-obvious) unfair cost sharing mechanism, at least for the fractional version of the problem. Our second contribution is showing how to implement our cost sharing mechanism which guarantees fast convergence to a near-optimum equilibrium. We show that for the fractional network design problems, there are indeed such mechanisms that induce greedy agents to converge to (1 + epsilon)-approximate equilibria in linear time.
