Rapid growth, fierce competition, and repeated failures of bike-sharing companies in the market highlight urgent needs for a systematic modeling framework to analyze optimal investment and management strategies of bike-sharing companies under competition. The share of bike-sharing market depends on how the competing companies deploy their bikes over time and space since travelers typically choose the nearest available bikes. Hence, each individual company aims to maximize its profit through optimal investment and allocation/rebalancing strategies in response to time-varying demand as well as actions of the peer companies. In this paper, we propose a game-theoretical framework to model the competition between two bike-sharing companies, and a two-stage multi-period stochastic program is developed to model the decision process of each company. The effects of demand elasticity and uncertainty are also discussed. We then show existence of Nash equilibrium and insights into the solution for several special cases. For general cases, an iterative algorithm is proposed to solve the Nash equilibrium. Numerical experiments are conducted to demonstrate the applicability of the proposed model and to draw insights on the impacts of market competition.

快速增长，激烈的竞争以及共享单车公司在市场上的反复失败，凸显了对系统模型框架的迫切需求，以分析竞争中的共享单车公司的最佳投资和管理策略。共享单车市场的份额取决于竞争公司在时间和空间上如何部署自己的单车，因为旅行者通常会选择最接近的单车。因此，每个公司都旨在通过响应时间变化的需求以及同行公司的行动，通过最佳的投资和分配/再平衡策略来最大化其利润。在本文中，我们提出了一个博弈论框架来对两个共享单车公司之间的竞争进行建模，并开发了一个两阶段的多周期随机程序来对每个公司的决策过程进行建模。还讨论了需求弹性和不确定性的影响。然后，我们显示Nash平衡的存在以及对几种特殊情况的解决方案的见解。对于一般情况，提出了一种迭代算法来求解纳什均衡。进行了数值实验，以证明所提出模型的适用性，并就市场竞争的影响得出见解。