Global Stabilization of Nash Equilibrium for Mixed Traffic

We consider a traffic network in which the traffic is a mix of regular and connected-autonomous vehicles. We presume the headways for vehicles in each link in the network are distinct for the regular and autonomous vehicles, and the autonomous vehicle headways differ depending on type of vehicle being followed. We analyze the network in the context of a population game, with each population corresponding to an origin-destination pair and vehicle type. We assume the evolutionary dynamics of each population distribution are governed by an Impartial Pairwise Comparison (IPC) Protocol. For the regular vehicles, we presume the payoff mechanism is the negative of the travel time. For the autonomous vehicles, we presume the payoff mechanism is an algorithm that is controlled centrally, using feedback about the current state of the system. For this scenario, we propose a dynamic payoff control algorithm for the autonomous vehicles that guarantees global convergence to Nash equilibrium. Additionally, the algorithm assures that in steady-state, the regular and autonomous vehicles for each origin-destination pair equilibrate to the same optimum routes.