Stackelberg Routing of Autonomous Cars in Mixed-Autonomy Traffic Networks

As autonomous cars are becoming tangible technologies, road networks will soon be shared by human-driven and autonomous cars. However, humans normally act selfishly which may result in network inefficiencies. In this work, we study increasing the efficiency of mixed-autonomy traffic networks by routing autonomous cars altruistically. We consider a Stackelberg routing setting where a central planner can route autonomous cars in the favor of society such that when human-driven cars react and select their routes selfishly, the overall system efficiency is increased. We develop a Stackelberg routing strategy for autonomous cars in a mixed-autonomy traffic network with arbitrary geometry. We bound the price of anarchy that our Stackelberg strategy induces and prove that our proposed Stackelberg routing will reduce the price of anarchy, i.e. it increases the network efficiency. Specifically, we consider a non-atomic routing game in a mixed-autonomy setting with affine latency functions and develop an extension of the SCALE Stackelberg strategy for mixed-autonomy networks. We derive an upper bound on the price of anarchy that this Stackelberg routing induces and demonstrate that in the limit, our bound recovers the price of anarchy bounds for networks of only human-driven cars.