Theoretically Founded Optimization of Auctioneer’s Revenues in Expanding Auctions

Abstract

The expanding auction is a multi-unit auction which provides the auctioneer with control over the outcome of the auction by means of dynamically adding items for sale. Previous research on the expanding auction has provided a numeric method to calculate a strategy that optimizes the auctioneer’s revenue. In this paper, we analyze various theoretical properties of the expanding auction, and compare it to VCG, a multi-unit auction protocol known in the art. We examine the effects of errors in the auctioneer’s estimation of the buyers’ maximal bidding values and prove a theoretical bound on the ratio between the revenue yielded by the Informed Decision Strategy (IDS) and the post-optimal strategy. We also analyze the relationship between the auction step and the optimal revenue and introduce a method of computing this optimizing step. We further compare the revenues yielded by the use of IDS with an expanding auction to those of the VCG mechanism and determine the conditions under which the former outperforms the latter. Our work provides new insight into the properties of the expanding auction. It further provides theoretically founded means for optimizing the revenue of auctioneer.