Collusion, efficiency, and dominant strategies

Green and Laffont [1] have proven that no collusion-resilient dominant-strategy mechanism guarantees efficiency in multi-unit auctions if a player is allowed to report only a single valuation. Chen and Micali [2] have bypassed this impossibility by slightly enlarging the strategy spaces, but via mechanisms that can impose impractically high fines. For unrestricted combinatorial auctions, the possibility of guaranteeing efficiency in collusion-resilient dominant strategies has remained open. In this paper, we (a) generalize the notion of a collusion-resilient dominant-strategy mechanism by allowing for arbitrary strategy spaces, (b) construct such a mechanism for multi-unit auctions which is highly practical, and (c) prove that no such mechanism, practical or not, exists for unrestricted combinatorial auctions. Our results hold in the very general collusion model of Green and Laffont, where the mechanism does not know who colludes with whom, a player may or may not have information about players with whom he does not collude, and players belonging to the same coalition can make side payments to each other and perfectly coordinate their strategies. ∗Supported by Fannie and John Hertz Foundation Daniel Stroock Fellowship.