Analysis of Nash and Stackelberg Equilibria of Autonomous Mobility-on-Demand Systems in Mixed Traffic

This paper analyzes the differences between Nash and Stackelberg equilibria of Autonomous Mobility-on-Demand (AMoD) systems in mixed traffic conditions, whereby self-driving robotaxis provide on-demand mobility, possibly pooling users together, while sharing the road with selfish private cars. In particular, we first introduce the optimal fleet routing problem in mixed traffic conditions, considering a car-road network where also private, selfish vehicles are present. Second, we model the interactions between the centrally controlled AMoD fleet and the private cars with two equilibrium formulations: the first corresponds to a Nash equilibrium, where each agent (the fleet and the private users) reacts to the other agent’s action until convergence is reached. For the second approach, corresponding to a Stackelberg equilibrium, the leader (the fleet) can predict the best response of the follower (private users) and plan the strategy accordingly. The results of a case study of Sioux Falls, USA, indicate that the two equilibria are very similar in terms of the fleet’s objective function, suggesting that even if the operator can predict the best response of the private users, no benefit arises.