Optimal investment and management of shared bikes in a competitive market

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.