Optimizing on-demand ride-hailing services in two-sided coupled markets with impatient riders

This paper examines the optimal design of dynamic pricing strategies for a coupled ride-hailing market with the coexistence of ridesharing and non-ridesharing services. Riders may switch between ridesharing and non-ridesharing alternatives to maximize individual utility, which results in demand diversion. Due to the imbalance between demand and supply, riders may become impatient towards long waiting times, leading to reneging in the coupled ride-hailing systems. We first establish dynamic meeting models for ridesharing and non-ridesharing separately to characterize temporal matching patterns. Meantime, the demand diversion generated by rider switching and reneging rate resulting from rider impatience towards waiting times are integrated into the dynamic meeting models. We derive the conditions on trip fares and commission rates to ensure the existence of the coupled ride-hailing market. We then analyze the effects of the dynamic pricing strategy on the market characteristics, including waiting times and market demand. Moreover, we formulate a Markov Decision Process (MDP) model to optimize dynamic pricing strategies and the corresponding aggregated matching between demand and supply. Finally, we develop the Proximal Policy Optimization (PPO) algorithm to solve the proposed MDP model and an iteration method that uses a Lookahead algorithm to estimate the market state. Our numerical experiments reveal that higher trip fares and commission rates should be adopted under the optimal dynamic pricing strategy compared to the fixed pricing strategy. We also demonstrate the effectiveness of dynamic pricing strategy in improving system performance and matching rate. If riders are more patient with waiting times, the platform operator can improve the trip fares for ridesharing riders to better manage demand, which helps to enhance the matching rate. Meantime, both the reneging rate and the level of demand diversion can be decreased.