Title: Repositioning, Ride-matching, and Abandonment in On-demand Ride-hailing Platforms: A Mean Field Game Approach Show Chinese title

Title: 按需网约车平台中的重新定位、拼车和放弃：基于平均场博弈的方法

Abstract: The on-demand ride-hailing industry has experienced rapid growth, transforming transportation norms worldwide. Despite improvements in efficiency over traditional taxi services, significant challenges remain, including drivers' strategic repositioning behavior, customer abandonment, and inefficiencies in dispatch algorithms. To address these issues, we introduce a comprehensive mean field game model that systematically analyzes the dynamics of ride-hailing platforms by incorporating driver repositioning across multiple regions, customer abandonment behavior, and platform dispatch algorithms. Using this framework, we identify all possible mean field equilibria as the Karush-Kuhn-Tucker (KKT) points of an associated optimization problem. Our analysis reveals the emergence of multiple equilibria, including the inefficient "Wild Goose Chase" one, characterized by drivers pursuing distant requests, leading to suboptimal system performance. To mitigate these inefficiencies, we propose a novel two-matching-radius nearest-neighbor dispatch algorithm that eliminates undesirable equilibria and ensures a unique mean field equilibrium for multi-region systems. The algorithm dynamically adjusts matching radii based on driver supply rates, optimizing pick-up times and waiting times for drivers while maximizing request completion rates. Numerical experiments and simulation results show that our proposed algorithm reduces customer abandonment, minimizes waiting times for both customers and drivers, and improves overall platform efficiency. Show Chinese abstract

Abstract: 按需叫车行业经历了快速增长，改变了全球的交通规范。 尽管相较于传统的出租车服务，在效率上有所提升，但仍存在显著挑战，包括司机的战略性重新定位行为、客户流失以及调度算法中的低效问题。 为了解决这些问题，我们引入了一个全面的平均场博弈模型，通过整合多个区域内的司机重新定位、客户的流失行为以及平台的调度算法，系统地分析了叫车平台的动态。 利用这一框架，我们将所有可能的平均场均衡识别为相关优化问题的 Karush-Kuhn-Tucker (KKT) 点。 我们的分析揭示了多种均衡的存在，其中包括由司机追逐遥远订单所导致的低效“徒劳追逐”均衡，这种均衡会导致系统性能不佳。 为了缓解这些低效问题，我们提出了一种新颖的双匹配半径最近邻调度算法，该算法消除了不理想的均衡，并确保多区域系统的唯一平均场均衡。 该算法根据司机供应率动态调整匹配半径，优化司机的接单时间和等待时间，同时最大化请求完成率。 数值实验和仿真结果显示，我们提出的算法减少了客户流失，最小化了客户和司机的等待时间，并提高了整体平台效率。