Selfish Routers and the Price of Anarchy

We revisit Roughgarden and Tardos’s price of anarchy in network routing, in a new model in which routing decisions are made by the edges as opposed to the flows. We propose two models: the latency model in which 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 edges advertise pricing schemes to their neighbors and seek to maximize their profit. We show the counterintuitive result that the price of stability in the latency model is Ω(n 1 60 ), even with linear latencies (as compared with 4 3 for the case in which routing decisions are made by the flows themselves). However, in the pricing model in which edges advertise pricing schemes — functions dictating how the price varies as a function of the total amount of flow — we show the surprising result that, under a condition ruling out monopolistic situations, all Nash equilibria have societally optimal flows; that is, the price of anarchy in this model is one. ? University of California, Berkeley. Email: [email protected]. ?? University of California, Berkeley. Work supported under a National Science Foundation Graduate Research Fellowship. Email: [email protected].