Design of discrete Dutch auctions with an uncertain number of bidders

The focus of this paper is on Dutch auctions where the bidding prices are restricted to a finite set of values and the number of bidders follows a Poisson distribution. The goal is to determine what the discrete bid levels should be to maximize the auctioneer’s expected revenue, which is the same as the average selling price of the object under consideration. We take a new approach to the problem by formulating the descending‐price competitive bidding process as a nonlinear program. The optimal solution indicates that the interval between two successive bids should be wider as the Dutch auction progresses. Moreover, the auctioneer’s maximum expected revenue increases with the number of bid levels to be set as well as the expected number of bidders. Numerical examples are provided to illustrate the key results from this study and their managerial implications are discussed.