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Published October 2014 | public
Book Section - Chapter

Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions


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.

Additional Information

© 2014 IEEE. We thank Éva Tardos for useful discussions. UB was supported by a Linde/SISL postdoctoral fellowship and NSF grants CNS-0846025, CCF-1101470 and EPAS-1307794. KL was supported by the Charles Lee Powell Foundation and a Microsoft Faculty Fellowship. LJS was supported by NSF grants 1038578 and 1319745, and was partly at the Simons Institute at UC Berkeley. CS was supported by NSERC grant 32760-06, an NSERC Discovery Accelerator Supplement Award, and an Ontario Early Researcher Award.

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August 22, 2023
October 25, 2023