Marginal cost pricing with a fixed error factor in traffic networks

It is well known that charging marginal cost tolls (MCT) from self interested agents participating in a congestion game leads to optimal system performance, i.e., minimal total latency. However, it is not generally possible to calculate the correct marginal costs tolls precisely, and it is not known what the impact is of charging incorrect tolls. This uncertainty could lead to reluctance to adopt such schemes in practice. This paper studies the impact of charging MCT with some fixed factor error on the system's performance. We prove that under-estimating MCT results in a system performance that is at least as good as that obtained by not applying tolls at all. This result might encourage adoption of MCT schemes with conservative MCT estimations. Furthermore, we prove that no local extrema can exist in the function mapping the error value, r, to the system's performance, T(r). This result implies that accurately calibrating MCT for a given network can be done by identifying an extremum in T(r) which, consequently, must be the global optimum. Experimental results from simulating several large-scale, real-life traffic networks are presented and provide further support for our theoretical findings.