  We study the equilibrium behavior in a multi-commodity selfish routing game
with many types of uncertain users where each user over- or under-estimates
their congestion costs by a multiplicative factor. Surprisingly, we find that
uncertainties in different directions have qualitatively distinct impacts on
equilibria. Namely, contrary to the usual notion that uncertainty increases
inefficiencies, network congestion actually decreases when users over-estimate
their costs. On the other hand, under-estimation of costs leads to increased
congestion. We apply these results to urban transportation networks, where
drivers have different estimates about the cost of congestion. In light of the
dynamic pricing policies aimed at tackling congestion, our results indicate
that users' perception of these prices can significantly impact the policy's
efficacy, and "caution in the face of uncertainty" leads to favorable network
conditions.
