Characterization of strategy-proof, revenue monotone combinatorial auction mechanisms and connection with false-name-proofness

A combinatorial auction mechanism consists of an allocation rule and a payment rule. There have been several studies on characterizing strategy-proof allocation rules. In particular, conditions called weak-monotonicity has been identified as a full characterization of them. On the other hand, revenue monotonicity is recognized as one of the desirable properties. A combinatorial auction mechanism is revenue monotone if a seller's revenue is guaranteed to weakly increase as the number of bidders grows. Though the property is quite reasonable, there exists virtually no work on the characterization. In this paper, we identified a simple condition called summation-monotonicity. We then proved that we can construct a strategy-proof, revenue monotone mechanism if and only if the allocation rule satisfies weak-monotonicity and summation-monotonicity. To the best of our knowledge, this is the first attempt to characterize revenue monotone allocation rules. In addition, we shed light on a connection between revenue monotonicity and false-name-proofness. In fact, we proved that, assuming a natural condition, revenue monotonicity is equivalent to false-name-proofness for single-item auctions.