Toward System-Optimal Routing in Traffic Networks: A Reverse Stackelberg Game Approach

In the literature, several road pricing methods based on hierarchical Stackelberg games have been proposed to reduce congestion in traffic networks. We propose three novel schemes to apply the extended reverse Stackelberg game, through which traffic authorities can induce drivers to follow routes that are computed to reach a system-optimal distribution of traffic on the available routes of a freeway, e.g., to minimize the total time spent of traffic in the network and to reduce traffic emissions in urban traffic networks. In this game-theoretical approach, the leader player representing the traffic authority communicates with the followers (drivers) via an onboard computer, in which the main instrument of the leader is the so-called leader function. This function maps the follower's decision space into the leader's decision space, resulting in a leader decision that is directly dependent on the follower's decision variables. Compared with the original game, we can rely on solution methods developed for the general reverse Stackelberg game and show that a system-optimal behavior can be reached, while taking heterogeneous driver classes into account.