Vehicle sharing systems are among the most promising intermediate transport modes for promoting environmentally friendly and resource-efficient mobility. A challenge when operating such systems is to ensure that enough vehicles are present at every station so as to respond adequately to the demand. In this work, we consider a station-based one-way vehicle sharing system, like, e.g., Vélib, but, contrary to this latter, we assume the rebalancing exclusively achieved by inciting the users to sometimes modify their destination stations, so as to reroute the flow of vehicles. Prices attached to the stations are used for the incitation: the amount to pay for a ride is the price attached to the destination station. A user arriving at an origin station may not perform a ride only for two reasons: either there is no available vehicle at the station when he arrives, or the current prices attached to the stations make him prefer to walk.

We formalize the pricing problem on a streamlined system as an optimization problem aiming at maximize the proportion of users who eventually take a ride, and with decision variables the prices attached to the stations. We consider a static version, where the prices cannot change over time, and a dynamic version, where the prices can change over time, depending on the current status of the system. Static prices are used in practice in several places, e.g., in Paris, but dynamic prices are more seldom (one example is Ekar, in Saoudi Arabia).