Network resource allocation and a congestion game: the single link case

We explore the properties of a congestion game where users of a congested resource anticipate the effect of their actions on the price of the resource. When users are sharing a single resource, we show existence and uniqueness of the Nash equilibrium, and establish that the aggregate utility received by the users is at least 3/4 of the maximum possible aggregate utility. These results form part of a growing literature on the "price of anarchy," i.e., the extent to which selfish behavior affects system efficiency.