  We study the worst-case welfare of item pricing in the \emph{tollbooth
problem}. The problem was first introduced by Guruswami et al, and is a special
case of the combinatorial auction in which (i) each of the $m$ items in the
auction is an edge of some underlying graph; and (ii) each of the $n$ buyers is
single-minded and only interested in buying all edges of a single path. We
consider the competitive ratio between the hindsight optimal welfare and the
optimal worst-case welfare among all item-pricing mechanisms, when the order of
the arriving buyers is adversarial. We assume that buyers own the
\emph{tie-breaking} power, i.e. they can choose whether or not to buy the
demand path at 0 utility. We prove a tight competitive ratio of $3/2$ when the
underlying graph is a single path (also known as the \emph{highway} problem),
whereas item-pricing can achieve the hindsight optimal if the seller is allowed
to choose a proper tie-breaking rule to maximize the welfare. Moreover, we
prove an $O(1)$ upper bound of competitive ratio when the underlying graph is a
tree.
  For general graphs, we prove an $\Omega(m^{1/8})$ lower bound of the
competitive ratio. We show that an $m^{\Omega(1)}$ competitive ratio is
unavoidable even if the graph is a grid, or if the capacity of every edge is
augmented by a constant factor $c$. The results hold even if the seller has
tie-breaking power.
