Optimal Cost-Sharing in Weighted Congestion Games

We identify how to share costs locally in weighted congestion games with polynomial cost functions to minimize the worst-case price of anarchy (POA). First, we prove that among all cost-sharing methods that guarantee the existence of pure Nash equilibria, the Shapley value minimizes the worst-case POA. Second, if the guaranteed existence condition is dropped, then the proportional cost-sharing method minimizes the worst-case POA over all cost-sharing methods. As a byproduct of our results, we obtain the first POA analysis of the simple marginal contribution cost-sharing rule, and prove that marginal cost taxes are ineffective for improving equilibria in (atomic) congestion