Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions
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 desired 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. 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 seriesparallel networks, and singlecommodity routing games with linear latency functions, and complement these with a querycomplexity lower bound. We also obtain strong positive results for Stackelberg routing to achieve target equilibria in seriesparallel 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 seriesparallel graphs; and sensitivity of equilibrium flow with respect to tolls. Our results demonstrate that one can indeed circumvent the potentiallyonerous task of modeling latency functions, and yet obtain meaningful results for the underlying routing game.
 Publication:

arXiv eprints
 Pub Date:
 August 2014
 arXiv:
 arXiv:1408.1429
 Bibcode:
 2014arXiv1408.1429B
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Data Structures and Algorithms
 EPrint:
 36 pages, 3 figures