A New Look at Selfish Routing

We revisit price of anarchy in network routing, in a new model in which routing decisions are made by self-interested components of the network, as opposed to by the flows as in [12]. This significant departure from previous work on the problem seeks to model Internet routing more accurately. We propose two models: the latency model in which the network edges seek to minimize the average latency of the flow through them on the basis of knowledge of latency conditions in the whole network, and the pricing model in which network edges advertise pricing schemes to their neighbors and seek to maximize their profit. We show two rather surprising results: the price of stability in the latency model is unbounded — Ω(n 1 60 ) — even with linear latencies (as compared with 3 in [12] for the case in which routing decisions are made by the flows themselves). However, in the pricing model in which edges advertise pricing schemes — how the price varies as a function of the total amount of flow — we show that, under a condition ruling out monopolistic situations, all Nash equilibria have optimal flows; that is, the price of anarchy in this model is one, in the case of linear latencies with no constant term.