Characterizing false-name-proof allocation rules in combinatorial auctions

A combinatorial auction mechanism consists of an allocation rule that defines the allocation of goods for each agent, and a payment rule that defines the payment of each winner. There have been several studies on characterizing strategy-proof allocation rules. In particular, a condition called weak-monotonicity has been identified as a full characterization of strategy-proof allocation rules. More specifically, for an allocation rule, there exists an appropriate payment rule so that the mechanism becomes strategy-proof if and only if it satisfies weak-monotonicity. In this paper, we identify a condition called sub-additivity which characterizes false-name-proof allocation rules. False-name-proofness generalizes strategy-proofness, by assuming that a bidder can submit multiple bids under fictitious identifiers. As far as the authors are aware, this is the first attempt to characterize false-name-proof allocation rules. We can utilize this characterization for developing a new false-name-proof mechanism, since we can concentrate on designing an allocation rule. As long as the allocation rule satisfies weak-monotonicity and sub-additivity, there always exists an appropriate payment rule. Furthermore, by utilizing the sub-additivity condition, we can easily verify whether a mechanism is false-name-proof. To our surprise, we found that two mechanisms, which were believed to be false-name-proof, do not satisfy sub-additivity; they are not false-name-proof. As demonstrated in these examples, our characterization is quite useful for mechanism verification.