Abstract: The allocation of scarce capacity is not uncommon in industries where surging demand exceeding the capacity occurs and expanding the capacity is costly or time-consuming.A system that consists of one supplier and two independent retailers is considered. Given that the supplier has limited capacity, retailers may compete for the capacity for profitability considerations. The wholesale price of products selling to retailers is given exogenously. In this paper a new capacity allocation rule, priority auction mechanism, is developed where the supplier sells the priority of allocation as the object in an auction, prioritizes retailers depending on their bids, and satisfies retailers’ order following their priority. It is derived that the priority auction is a common value auction model in which the value of allocation priority is defined as the profit difference between two scenarios where any retailer is granted the priority or not. Two types of priority auction rules are proposed that different in the sequence of ordering and auction: ex-ante priority auction and ex-post priority auction. In the ex-ante priority auction, retailers need to submit their bids firstly and then place the order after the allocation sequence is determined by the auction. Thus, each retailers’ demand is still private information when they submit bids.In the ex-post priority auction, retailers first place the order and then participate in the auction if their total demand exceeds supplier’s capacity. Therefore, all retailers’ demand information is public in the auction. It is found that both the two types of priority auction are truth-telling mechanism, leading to the truthful reporting of retailers’ private demand information by their orders, and the classical revenue equivalence theorem still holds. Specifically, it is shown that the winner curse only occurs when the supplier adopts the first price sealed auction in ex-ante priority auction. Although the ex-post priority auction can help retailers avoid winner curse, because of the disclosure of retailers’ demand information before the auction, the supplier obtains a higher expected profit from ex-post priority auction than ex-ante priority auction. Priority auction mechanism guides a new way for the supplier to allocate the scarce capacity using the simple classical auction theory and improve the profit.

Key words: capacity allocation; priority auction; common value model; price discrimination