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

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

15 Scopus citations

Abstract

The analysis of network routing games typically assumes, right at the onset, precise and 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 desirable target flow as the equilibrium by suitably influencing player behavior in the routing game. We ask whether one can achieve target flows as equilibria without knowing the underlying latency functions. Our main result gives a crisp positive answer to this question. We show that, under fairly general settings, 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 candidate tolls as input and returns the resulting equilibrium flow. This result is obtained via a novel application of the ellipsoid method, and applies to arbitrary multicommodity settings and non-linear latency functions. Our algorithm extends easily to many other settings, such as (i) when certain edges cannot be tolled or there is an upper bound on the total toll paid by a user, and (ii) general nonatomic congestion games. We obtain tighter bounds on the query complexity for series-parallel networks, and single-commodity routing games with linear latency functions, and complement these with a query-complexity lower bound applicable even to single-commodity routing games on parallel-link graphs with linear latency functions. We also explore the use of Stackelberg routing to achieve target equilibria and obtain strong positive results for series-parallel graphs. Our results build upon various new techniques that we develop pertaining to the computation of, and connections between, different notions of approximate equilibrium, properties of multicommodity flows and tolls in series-parallel graphs, and sensitivity of equilibrium flow with respect to tolls. Our results demonstrate that one can indeed circumvent the potentially-onerous task of modeling latency functions, and yet obtain meaningful results for the underlying routing game.

Original languageAmerican English
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
PublisherIEEE Computer Society
Pages31-40
Number of pages10
ISBN (Electronic)9781479965175
DOIs
StatePublished - 7 Dec 2014
Externally publishedYes
Event55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 - Philadelphia, United States
Duration: 18 Oct 201421 Oct 2014

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014
Country/TerritoryUnited States
CityPhiladelphia
Period18/10/1421/10/14

Bibliographical note

Publisher Copyright:
© 2014 IEEE.

Keywords

  • Network routing
  • Stackelberg routing
  • approximate equilibria
  • ellipsoid method
  • multicommodity flows
  • tolls

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