Revenue monotonicity in deterministic, dominant-strategy combinatorial auctions

Abstract

In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic, dominant-strategy combinatorial auction mechanisms. Our main result is that such failures of “revenue monotonicity” can occur under any such mechanism that is weakly maximal—meaning roughly that it chooses allocations that cannot be augmented to cause a losing bidder to win without hurting winning bidders—and that allows bidders to express arbitrary known single-minded preferences. We also give a set of other impossibility results as corollaries, concerning revenue when the set of goods changes, false-name-proofness, and the core. 1 1 We previously published a six-page preliminary version of our main result at a conference (Rastegari et al., 2007) [24]. Among other differences, this work considered a very limited version of our weak maximality condition that can be understood as requiring Pareto efficiency with respect to bidder valuations (i.e., ignoring payments).