A great challenge of city planners is to provide efficient and effective connection service to travelers using public transportation system. This is commonly known as the last-mile problem and is critical in promoting the utilization of public transportation system. In this paper, we address the last-mile problem by considering a dynamic and demand-responsive mechanism for arranging ride sharing on a non-dedicated commercial fleet (such as taxis or passenger vans). Our approach has the benefits of being dynamic, flexible, and with low setup cost. A critical issue in such ride-sharing service is how riders should be grouped and serviced, and how fares should be split. We propose two auction designs which are used to solicit individual rider's willing payment rate and compensation rate (for extra travel, if any). We demonstrate that these two auctions are budget balanced, individually rational, and incentive compatible. A series of experimental studies based on both synthetic and real-world datasets are designed to demonstrate the pros and cons of our two proposed auction mechanisms in various settings.