Transport network pricing is a topic of interest to transport planners and users alike. Pricing schemes are a vital traffic management strategy which can be implemented to reduce congestion, among other network externalities. Previous research has explored pricing schemes to achieve a variety of network objectives, including social and environmental concerns. This work introduces a robust strategic system optimal (StrSO) pricing scheme which incorporates a novel user equilibrium-based behavioural model, specifically the strategic traffic equilibrium (StrUE) model. Prices are set on all links in a network to improve expected system performance by lowering expected system travel time, thus relieving congestion. The proposed solution method is scalable to large networks. The results show how the introduced measures of system performance can be used to investigate the relationship between congestion and reliability in the tolled network.