Multi-unit double auction under group buying

![CDATA[Group buying is a business model in which a number of buyers join together to make an order of a product in a certain quantity in order to gain a desirable discounted price. Such a business model has recently received significant attention from researchers in economics and computer science, mostly due to its successful application in online businesses, such as Groupon. This paper deals with the market situation when multiple sellers sell a product to a number of buyers with discount for group buying. We model this problem as a multi-unit double auction. We first examine two deterministic mechanisms that are budget balanced, individually rational and only one-sided truthful, i.e. it is truthful for either buyers or sellers. Then we find that, although there exists a “trivial” (non-deterministic) mechanism that is (weakly) budget balanced, individually rational and truthful for both buyers and sellers, such a mechanism is not achievable if we further require that both the trading size and the payment are neither seller-independent nor buyer-independent. In addition, we show that there is no budget balanced, individually rational and truthful mechanism that can also guarantee a reasonable trading size.]]