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

TL;DR

This paper compares the effectiveness of subsidies and tolls in congestion games, showing that subsidies can be as effective as tolls under certain conditions but may perform worse with user heterogeneity, supported by theoretical bounds.

Contribution

It provides a comparative analysis of subsidies versus tolls in congestion games, including explicit performance bounds and the impact of user heterogeneity.

Findings

Subsidies perform similarly to tolls when users are predictable.

Tolls outperform subsidies in heterogeneous user scenarios.

Explicit bounds are derived for both methods in affine congestion games.

Abstract

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.