Revenue Monotonicity in Combinatorial Auctions

Baharak Rastegari, Anne Condon, Kevin Leyton-Brown

Abstract: Intuitively, one might expect that a seller's revenue from an auction weakly increases as the number of bidders grows, as this increases competition. However, it is known that for combinatorial auctions that use the VCG mechanism, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this problem can occur under other dominant-strategy combinatorial auction mechanisms. Our main result is that such failures of "revenue monotonicity" are not limited to mechanisms that achieve efficient allocations. Instead, they can occur under any dominant-strategy direct mechanism that sets prices using critical values, and that always chooses an allocation that cannot be augmented to make some bidder better off, while making none worse off.