A mean-field Markov decision process model for spatial-temporal subsidies in ride-sourcing markets

Ride-sourcing services are increasingly popular because of their ability to accommodate on-demand travel needs. A critical issue faced by ride-sourcing platforms is the supply-demand imbalance, as a result of which drivers may spend substantial time on idle cruising and picking up remote passengers. Some platforms attempt to mitigate the imbalance by providing relocation guidance for idle drivers who may have their own self-relocation strategies and decline to follow the suggestions. Platforms then seek to induce drivers to system-desirable locations by offering them subsidies. This paper proposes a mean-field Markov decision process (MF-MDP) model to depict the dynamics in ride-sourcing markets with mixed agents, whereby the platform aims to optimize some objectives from a system perspective using spatial-temporal subsidies with predefined subsidy rates, and a number of drivers aim to maximize their individual income by following certain self-relocation strategies. To solve the model more efficiently, we further develop a representative-agent reinforcement learning algorithm that uses a representative driver to model the decision-making process of multiple drivers. This approach is shown to achieve significant computational advantages, faster convergence, and better performance. Using case studies, we demonstrate that by providing some spatial-temporal subsidies, the platform is able to well balance a short-term objective of maximizing immediate revenue and a long-term objective of maximizing service rate, while drivers can earn higher income.