Achieving System-Optimal Splitting Rates in a Freeway Network Using a Reverse Stackelberg Approach

A game-theoretical method is proposed to achieve a system-optimal distribution of traffic over a freeway network. In particular, the road authority is represented by a leader player and each follower player embodies a group of drivers with the same value of time that plan to travel between a given origin and destination. In the proposed reverse Stackelberg approach, the leader presents a function to each follower that maps a vector of splitting rates over possibles routes to a monetary incentive. The follower then decides upon a splitting rate and the associated monetary incentive that yield the minimum weighted measure of travel time and monetary fees. In this manner, the road authority can compose an optimal leader function under which the followers will behave as desired, i.e., to achieve the system-optimal splitting rates.