Network Topology and the Efficiency of Equilibrium

Igal Milchtaich

Games and Economic Behavior 57 (), 321–346


Different kinds of networks, such as transportation, communication, computer, and supply networks, are susceptible to similar kinds of inefficiencies. These arise when congestion externalities make the cost for each user depend on the other users’ choice of routes. If each user chooses the least expensive (e.g., the fastest) route from the users’ common point of origin to the common destination, the result may be Pareto inefficient in that an alternative choice of routes would reduce the costs for all users. Braess’s paradox represents an extreme kind of inefficiency, in which the equilibrium costs may be reduced by raising the cost curves. As this paper shows, this paradox occurs in an (undirected) two-terminal network if and only if it is not series-parallel. More generally, Pareto inefficient equilibria occur in a network if and only if one of three simple networks is embedded in it.

JEL classification

C72, R41


Congestion; Externalities; Topological efficiency; Nonatomic games; Network topology; Braess’s paradox; Transportation networks; Wardrop equilibrium