Space Booking with Multistage Online VCG Mechanism: A Simulation Study Toward Practical Application

Abstract

Most current reservation systems include only time slots as reservation information. Customers need only to make a reservation by choosing a proper time. The value generated by a reservation is unknown until the customers are served. Therefore, an important shortcoming of current reservation systems is that they require limited information from customers, engendering a loss of social welfare. We surmise that an innovative reservation system including space value can produce more desired outcomes by considering various factors, such as social distancing during a pandemic. Based on that supposition, we adopt the Vickrey–Clarke–Groves (VCG) mechanism to achieve social welfare maximization and strategy-proofness. To offset VCG mechanism shortcomings in practical applications, we converted the VCG mechanism to a multistage online VCG mechanism that can do timely processing of customers’ reservations and can thereby maximize social welfare. The multistage online VCG mechanism generates higher social welfare than most current reservation systems, which use a first-come, first-served mechanism. Additionally, we demonstrate that, by adjusting the VCG mechanism bid number to a practical level, the reservation process can be improved considerably with a probability of more than 99% for satisfying the strategy-proofness of the VCG mechanism. Funding: This work was supported by JSPS KAKENHI [Grant 22H01710] and the Mohammed bin Salman Center for Future Science and Technology for Saudi–Japan Vision 2030 at the University of Tokyo [Grant MbSC2030].