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We put forward a new mechanism achieving a high benchmark for (both revenue and) the sum of revenue and efficiency in truly combinatorial auctions. Notably, our mechanism guarantees its performance (1) in a very adversarial collusion model; (2) for any profile of strategies surviving the iterated elimination of dominated strategies; and (3) by leveraging the knowledge that the players have about each other (in a non-Bayesian setting).Our mechanism also is computationally efficient, and preserves the players' privacy to an unusual extent.
