Characterization of revenue monotonicity in combinatorial auctions

An auction mechanism consists of an allocation rule and a payment rule. There have been several studies on characterizing strategy-proof allocation rules; if the allocation rule satisfies a condition called weak-monotonicity, an appropriate payment rule is guaranteed to exist. One desirable property that an auction mechanism should satisfy is revenue monotonicity; a seller's revenue is guaranteed to weakly increase as the number of bidders grows. In this paper, we first identify a simple condition called summation-monotonicity for characterizing strategy-proof and revenue monotone allocation rules. To the best of our knowledge, this is the first attempt to characterize revenue monotone allocation rules. Based on this characterization, we also examine the connections between revenue monotonicity and false-name-proofness, which means a bidder cannot increase his utility by submitting multiple bids under fictitious names. In a single-item auction, we show that they are basically equivalent; a mechanism is false-name-proof if and only if it is strategy-proof and revenue monotone. On the other hand, we show these two conditions cannot coexist in combinatorial auctions under some minor condition.