On Stackelberg Strategy in Affine Congestion Games

We investigate the efficiency of some Stackelberg strategies in congestion games with affine latency functions. A Stackelberg strategy is an algorithm that chooses a subset of players and assigns them a prescribed strategy with the purpose of mitigating the detrimental effect that the selfish behavior of the remaining uncoordinated players may cause to the overall performance of the system. The efficiency of a Stackelberg strategy is measured in terms of the price of anarchy of the pure Nash equilibria they induce. Three Stackelberg strategies, namely Largest Latency First, Cover and Scale, were already considered in the literature and non-tight upper and lower bounds on their price of anarchy were given. We reconsider these strategies and provide the exact bound on the price of anarchy of both Largest Latency First and Cover and a better upper bound on the price of anarchy of Scale.