From Aggregate Observations to Social Optimum: An Adaptive Pricing Scheme in Heterogeneous Congestion Games

This study investigates an adaptive pricing scheme aimed at achieving an efficient state in a traffic congestion game characterized by a diverse population of road users. While the planner possesses knowledge of players' preferences, their ability to observe only aggregate states limits the implementation of differentiated taxes. We propose a pricing approach that aligns taxes with the true values of externalities over time, ensuring global stability of the social optimum through replicator dynamics. Our findings suggest that the planner, despite being unable to accurately assess externalities at each moment, can still navigate the economy toward a long-term social optimum by adjusting the disaggregated state based on aggregate observations, while acknowledging the challenges posed by heterogeneous value of time (VOT) among drivers. We also find that a pricing mechanism that incorporates the current externalities for each period, which could be executed by a planner with full access to the disaggregated state, might fail to achieve the global stability of the social optimum under the same dynamics.