In this paper, we introduce a novel class of non-cooperative games, in which a closed network of queues is shared between multiple players. Each player receives a reward based on the throughput of their jobs, while they incur a cost that varies with the number of jobs they submit. Closed queueing networks are a commonly used stochastic formalism that model a variety of real-world situations, and
this paper presents an application to competitive vehicle-sharing systems. In our vehicle-sharing system model, each provider receives revenue from each trip, but pays a cost based on the total number of vehicles. 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 apply this model to a case study of a hypothetical vehicle-sharing system in Oslo.
The results indicate that adding a single competitor can increase the number of trips taken by up to 14.1%, adding two competitors can increase the amount by up to 18.9%, and a highly competitive market can increase this by up to 30%.