Network topology and the efficiency of equilibrium

Different networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities render each user's cost dependent on the other users' choice of routes. If each user chooses the least expensive (e. g., fastest) route from the users' common point of origin to the common destination, the result may be inefficient in the sense that there is an alternative choice of routes that reduces the costs for all users. However, this may happen only for certain kinds of network topologies. This paper gives several alternative characterizations of networks in which inefficiencies may occur. In particular, a necessary and sufficient condition for inefficiency is that specific simple network is embedded in the network.