Network topology and the efficiency of equilibrium

Research output: Contribution to journalArticlepeer-review

79 Scopus citations


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.

Original languageEnglish
Pages (from-to)321-346
Number of pages26
JournalGames and Economic Behavior
Issue number2
StatePublished - Nov 2006

Bibliographical note

Funding Information:
✩ This research was supported by the Israel Science Foundation (Grant No. 749/02). E-mail address: URL:


  • Braess's paradox
  • Congestion
  • Externalities
  • Network topology
  • Nonatomic games
  • Topological efficiency
  • Transportation networks
  • Wardrop equilibrium


Dive into the research topics of 'Network topology and the efficiency of equilibrium'. Together they form a unique fingerprint.

Cite this