Revenue failures and collusion in combinatorial auctions and exchanges with vcg payments

In a combinatorial auction, there are multiple items for sale, and bidders are allowed to place a bid on a bundle of these items rather than just on the individual items. A key problem in this and similar settings is that of strategic bidding, where bidders misreport their true preferences in order to effect a better outcome for themselves. The VCG payment scheme is the canonical method for motivating the bidders to bid truthfully. We study two related problems concerning the VCG payment scheme: the problem of revenue guarantees, and that of collusion. The existence of such problems is known by many; in this paper, we lay out their full extent. We study four settings: combinatorial forward auctions with free disposal, combinatorial reverse auctions with free disposal, combinatorial forward (or reverse) auctions without free disposal, and combinatorial exchanges. In each setting, we give an example of how additional bidders (colluders) can make the outcome much worse (less revenue or higher cost) under the VCG payment scheme (but not under a first price scheme); derive necessary and sufficient conditions for such an effective collusion to be possible under the VCG payment scheme; and (when nontrivial) study the computational complexity of deciding whether these conditions hold.

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