  Are rewards or penalties more effective in influencing user behavior? This
work compares the effectiveness of subsidies and tolls in incentivizing users
in congestion games. The predominantly studied method of influencing user
behavior in network routing problems is to institute taxes which alter users'
observed costs in a manner that causes their self-interested choices to more
closely align with a system-level objective. Another feasible method to
accomplish the same goal is to subsidize the users' actions that are preferable
from a system-level perspective. We show that, when users behave similarly and
predictably, subsidies offer comparable performance guarantees to tolls while
requiring smaller monetary transactions with users; however, in the presence of
unknown player heterogeneity, subsidies fail to offer the same performance as
tolls. We further investigate these relationships in affine congestion games,
deriving explicit performance bounds under optimal tolls and subsidies with and
without user heterogeneity; we show that the differences in performance can be
significant.
