Balancing High Social Welfare and Short Waiting Times: Determining a Reasonable Buyout Price in Auction-Based Restaurant Reservation Systems

This study proposes an auction-based dynamic reservation system, the “synthetic scheduling auction” (SSA), to maximize social welfare through restaurant services. Each potential customer group submits 3-tuple bids to the restaurant, including the meal starting time, meal selection, and number of people in the group. After receiving these bids, the restaurant offers a buyout price to the group. To calculate the buyout price, the restaurant conducts an auction with synthetic customer agents who intend to book the restaurant within the reservation period. These agents are generated based on the restaurant’s past customer statistics data. The buyout price is the “expected nuisance fee” based on the money transfer function determined by the VCG mechanism applied for static auctions. By conducting an auction with synthetic customers, the restaurant determines the buyout price without waiting for actual future reservation applicants. Therefore, SSA achieves an increased social welfare than in the First-Come-First-Served (FCFS) reservation system, the current standard, and a decreased waiting time for each customer group compared with the static auction mechanism. Computer experiments were conducted on a fictitious restaurant to compare the social surplus and seat occupancy rates when the restaurant used the SSA and FCFS system. The results demonstrate that the SSA is superior in both metrics, that is, social surplus and seat occupancy rates.