Mobility sharing services are expected to solve several important issues such as global warming and efficient mobility. However, if the services allow users to take arbitrary trips, the overall efficiency of the service cannot be achieved. To solve this problem, this study proposes a tradable permit mechanism for such services. We first provide a model that describes the equilibrium under the proposed system and for socially optimal assignment, and then propose the Vickrey-Clarke-Groves mechanism for car sharing. With this mechanism, this tradable permits system satisfies the strategy-proof and the efficient allocation. Next, we assume that the users are single-minded bidders and, under this assumption, we show that the assignment problem is equivalent to the linear programming problem. In addition, the permits price is decomposed to the usage fee for leaving the port of origin and the income for arriving at the port of destination. As a result, it is possible to interpret this auction mechanism as an exchange economy based on the trip's OD demand between users.