用可微代理模拟设计动态定价，让共享单车自动平衡库存。

Bike-sharing systems are emerging in various cities as a new ecofriendly transportation system. In these systems, spatiotemporally varying user demands lead to imbalanced inventory at bicycle stations, resulting in additional relocation costs. Therefore, it is essential to manage user demand through optimal dynamic pricing for the system. However, optimal pricing design for such a system is challenging because the system involves users with diverse backgrounds and their probabilistic choices. To address this problem, we develop a differentiable agent-based simulation to rapidly design dynamic pricing in bike-sharing systems, achieving balanced bicycle inventory despite spatiotemporally heterogeneous trips and probabilistic user decisions. We first validate our approach against conventional methods through numerical experiments involving 25 bicycle stations and five time slots, yielding 100 parameters. Compared to the conventional methods, our approach obtains a more accurate solution with a 73% to 78% reduction in loss while achieving more than a 100-fold increase in convergence speed. We further validate our approach on a large-scale urban bike-sharing system scenario involving 289 bicycle stations, resulting in a total of 1156 parameters. Through simulations using the obtained pricing policies, we confirm that these policies can naturally induce balanced inventory without any manual relocation. Additionally, we find that the cost of discounts to induce the balanced inventory can be minimized by setting appropriate initial conditions.