Revenue monotonicity in combinatorial auctions

Abstract

In recent work [Rastegari et al. 2007a; 2007b] we study revenue properties of combinatorial auctions. Consider a well-known drawback of the famous VCG mechanism: a seller’s revenue can go down when bidders are added to an auction, contrary to the intuition that having more bidders should increase competition. Following an example due to Ausubel and Milgrom [2006], consider an auction with three bidders and two goods for sale. Suppose that bidder 2 wants both goods for the price of $2 billion whereas bidder 1 and bidder 3 are willing to pay $2 billion for the first and the second good respectively (see Figure 1). The VCG mechanism awards the goods to bidders 1 and 3 for the price of zero, yielding the seller zero revenue. However, in the absence of either bidder 1 or bidder 3, the revenue of the auction would be $2 billion. We say that an auction mechanism is revenue monotonic if the seller’s revenue is …