The impact of autonomous vehicles on ride-hailing platforms with strategic human drivers

Abstract

We consider a ride-hailing platform that operates a mixed fleet of autonomous vehicles (AVs) and conventional vehicles (CVs), where AVs are fully controlled by the platform and CVs are operated by self-interested human drivers. Each vehicle is modeled using a Markov Decision Process where the vehicle maximizes long-run average rewards by choosing its repositioning actions. The behavior of CVs corresponds to a large-scale game in which agents interact through resource constraints that result in fluid queues. To optimize the mixed AV–CV system for arbitrary networks, we formulate a bi-level optimization problem $\mathrm{OPT}$ in which the platform moves first by controlling the demand revealed to the CVs and subsequently assigning the optimal actions to the AVs, while the CVs react by forming an equilibrium characterized by the solution to a convex optimization problem. We prove several structural properties of the optimal solution and analyze simple heuristics, such as AV-first, where we solve for the optimal dispatch of AVs without taking into account the subsequent reaction of CVs. We also propose three numerical algorithms to solve $\mathrm{OPT}$, which is a non-convex non-smooth problem, and evaluate their performance for large networks. Finally, we use our computational tools to show some interesting trends in the optimal AV–CV fleet dimensioning when vehicle supply is exogenous and endogenous, and apply these results to New York City using demand and trip-time data from real-world taxi service datasets. Our results suggest that our model can be used to predict traffic behavior and optimize mixed-fleet deployment given topology and cost/reward information.