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We consider one-way vehicle sharing systems where customers can rent a car atone station and drop it off at another. The problem we address is to optimizethe distribution of cars, and quality of service, by pricing rentalsappropriately. We propose a bidding approach that is inspired from auctions andtakes into account the significant uncertainty inherent in the problem data(e.g., pick-up and drop-off locations, time of requests, and duration oftrips). Specifically, in contrast to current vehicle sharing systems, theoperator does not set prices. Instead, customers submit bids and the operatordecides whether to rent or not. The operator can even accept negative bids tomotivate drivers to rebalance available cars to unpopular destinations within acity. We model the operator's sequential decision-making problem as a\emph{constrained Markov decision problem} (CMDP) and propose and rigorouslyanalyze a novel two phase $Q$-learning algorithm for its solution. Numericalexperiments are presented and discussed.

Two Phase $Q-$learning for Bidding-based Vehicle Sharing