  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 series-parallel
networks, and single-commodity routing games with linear latency functions, and
complement these with a query-complexity lower bound. We also obtain strong
positive results for Stackelberg routing to achieve target equilibria in
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.
