Carrots or Sticks? The Effectiveness of Subsidies and Tolls in Congestion Games

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.