Rouwendal, J., Verhoef, E. and Knockaert, J. (2012). Give or take? Rewards versus charges for a congested bottleneck Regional Science and Urban Economics, 42(1-2):166--176.

This paper analyzes the possibilities to relieve traffic congestion using subsidies instead of Pigouvian taxes, as well as revenue-neutral combinations of rewards and taxes ('feebates'). The model considers a Vickrey-ADL model of bottleneck congestion with endogenous scheduling. With inelastic demand, a fine (time-varying) reward is found to be equivalent to a fine toll, and to a continuum of combinations of time-varying tolls and rewards, including fine feebates. When demand is price-sensitive, a reward becomes less attractive from the efficiency viewpoint, because it attracts additional users to the congested bottleneck. As a result, both the second-best optimal fraction of rewarded travelers in the scheme, and the relative efficiency that can be achieved with it, decrease when demand becomes more elastic. Our analytical and simulation results for coarse schemes reveal that a coarse reward is less effective than a coarse feebate, which is itself less effective than a coarse toll. The most efficient coarse system is the step toll, which is also allowed to be positive in the fringes of the peak. Despite the smaller efficiency gains, rewards and feebates may be attractive to use in circumstances where public and political acceptability of tolling is especially low, so that its implementation is unlikely, including the temporary use of price incentives in case of road works and large-scale events. {\textcopyright} 2011 Elsevier B.V.