Congestion derivatives for a traffic bottleneck with heterogeneous commuters

Deterministic congestion pricing has attracted most attentions in the literature. But little attention has been given to pricing under uncertainty, especially for heterogeneous commuters. In this paper, we investigate congestion externalities by considering commuters’ risk preferences and heterogeneity. In particular, when price involves exogenous uncertainty which is independent of both central authority and individual commuters, we are able to express commuters’ departure equilibria and the total social cost in closed-form in terms of the departure time and uncertainty. Moreover, we find that uncertainty will lead heterogeneous risk-averse commuters not only to avoid traveling at the time when uncertainty level is high, but also to deviate from their optimal departure sequence. Hence, we are able to show that uncertainty can tremendously increase the total social cost. Furthermore, we also prove that both the central planner and the market-base mechanism have the potential to reduce the total social cost and alter commuters’ departure behavior. Specifically, we find out that the central planner can always find a class of financial derivatives to induce the socially optimal departure behavior, while the market-based mechanism may do so at specific cases. Finally, numerical formulation and experiments are given to assess the robustness of our results for more general forms of uncertainties and derivatives.