Achieving target equilibria in network routing games without knowing the latency functions

Umang Bhaskar*, Katrina Ligett, Leonard J. Schulman, Chaitanya Swamy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


The analysis of network routing games typically assumes precise, detailed information about the latency functions. Such information may, however, be unavailable or difficult to obtain. Moreover, one is often primarily interested in enforcing a desired target flow as an equilibrium. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. We give a crisp positive answer to this question. We show that one can efficiently compute edge tolls that induce a given target multicommodity flow in a nonatomic routing game using a polynomial number of queries to an oracle that takes tolls as input and outputs the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and extends to various other settings. We obtain improved query-complexity bounds for series-parallel networks, and single-commodity routing games with linear latency functions. Our techniques provide new insights into network routing games.

Original languageAmerican English
Pages (from-to)533-569
Number of pages37
JournalGames and Economic Behavior
StatePublished - Nov 2019

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.


  • Ellipsoid algorithm
  • Network flows
  • Query complexity
  • Routing games
  • Stackelberg routing
  • Tolls


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