Multi-objective pricing for shared vehicle systems

We propose a framework for data-driven pricing in shared vehicle systems (such as bikesharing and carsharing) in which customers can pick up and drop off vehicles in different locations. This framework provides efficient algorithms with rigorous approximation guarantees for a wide class of objective functions (including welfare and revenue), and under a variety of constraints on the prices. An interesting class of constraints accommodated by this framework includes multi-objective settings in which the goal is to maximize some objective function subject to some lower bound on another objective function. An important representative of this class is the Ramsey pricing problem, i.e. maximize revenue subject to some lower bound on welfare. Compared to traditional item-pricing problems, pricing in shared vehicle systems is more challenging due to network externalities, wherein setting prices at one demand node may affect the supply at each other node in the network. To capture the system dynamics, we use a closed queueing model in which exogenous demand (obtained from data) can be modulated through pricing. We achieve our approximation guarantees by first projecting the problem to an infinite-supply setting, deriving optimal prices in this limit, and then bounding the performance of these prices in the finite-vehicle system. Our infinite-to-finite supply reduction is of independent interest since it holds for a broader class of objective functions, and applies even more generally than the pricing problems that we consider.