Competitive Analysis of Vehicle-Sharing Systems With Cournot Queueing Games

Product-form closed queueing networks are a useful formalism for analyzing the availability of vehicles within a vehicle sharing system with stochastic user behavior. However, existing models assume that the provider has full control over the system. In reality, competition between providers within a single geographic area is quite common. In this paper, we introduce a non-cooperative game that extends a closed queueing model into a competitive environment, in which players decide the number of jobs that they wish to submit. This can be used to model vehicle sharing systems with multiple providers, in which they receive fares from trips but are responsible for the costs of their own fleet. The core technical results of this paper include conditions that guarantee the existence of a pure Nash equilibrium, and an efficient equilibrium-finding algorithm. We then present a case study, using our model, of a vehicle sharing system in Oslo with multiple providers. In this case study, we find that adding an additional competitor can increase the number of trips by up to 18.9%, and a highly competitive market can increase this by up to 30%.