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.
Bibliographical noteFunding Information:
Supported in part by NSERC grant 32760-06, an NSERC Discovery Accelerator Supplement Award, and an Ontario Early Researcher Award.
Work performed in part while at the Department of Computing and Mathematical Sciences, California Institute of Technology, and at the Department of Combinatorics and Optimization, University of Waterloo. Work supported in part by a Linde/SISL postdoctoral fellowship, NSF grants CNS-0846025, CCF-1101470 and EPAS-1307794, and a Ramanujan Fellowship.Work supported in part by NSF grants 1254169 and 1518941, United States-Israel Binational Science Foundation Grant 2012348, the Charles Lee Powell Foundation, a grant from the HUJI Cyber Security Research Center in conjunction with the Israel National Cyber Directorate (INCD) in the Prime Minister's Office, a startup grant from Hebrew University's School of Computer Science, and a Microsoft Faculty Fellowship. This material is based upon work supported by the United States Air Force and DARPA under Contract No. FA8750-16-C-0022.Work supported in part by NSF grants 1038578, 1319745 and 1618795. Work performed in part at the Simons Institute for the Theory of Computing at UC Berkeley.Supported in part by NSERC grant 32760-06, an NSERC Discovery Accelerator Supplement Award, and an Ontario Early Researcher Award.
© 2018 Elsevier Inc.
- Ellipsoid algorithm
- Network flows
- Query complexity
- Routing games
- Stackelberg routing