Social coordination in unknown price-sensitive populations

In this paper, we investigate the relationship between uncertainty and a designer's ability to influence social behavior. Pigovian taxes are a common approach to social coordination. However, guaranteeing efficient behavior typically requires that the system designer has complete knowledge of the user population's sensitivity to taxation. In this paper, we explore the effect of relaxing this requirement in the context of congestion games with affine costs. Focusing on the class of scaled Pigovian taxes, we derive the optimal tolling scheme that minimizes the worst-case efficiency loss under uncertainty in user sensitivity. Furthermore, we derive explicit bounds which highlight how the level of uncertainty in sensitivity degrades performance.