Dynamic Mechanism Design Under Multi-Unit Demand for Online Auction

This paper presents the theory of dynamic sequential auctions which can be used for pricing and inventory control in online auction. Most theoretical treatments of auctions have assumed that buyers have unit demand, which didn´t conform to the real state. We characterize this model when a seller with C units to sell by the way of sequential auctions faces a finite time horizon T, buyers in each period have multi-unit demands, and each of them has uniform, independent, private value for the product.. The numbers of bidders in each period as well as the individual bidders´ valuations are random but stationary over time. There is a holding cost for inventory, advertising cost component, monitoring costs, and a unit cost for ordering more stock from an outside supplier .Backordering is not allowed. The seller must decide how to conduct its auctions and how to replenish its stock over time to maximize its profits. To achieve the optimal revenue, we analyze the optimal allocation, the optimal number of products to accept the optimal number of to reorder, and find a modified second-price auctions and a first-price auctions to achieve the optimal allocation policy.