Truthful Mechanisms for Exhibitions

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We consider the following combinatorial auction: Given a range space , and m bidders interested in buying only ranges in , each bidder j declares her bid . We give a deterministic truthful mechanism, when the valuations are single-minded: when is a collection of fat objects (respectively, axis-aligned rectangles) in the plane, there is a truthful mechanism with a 1 + ε- (respectively, ⌈logn⌉)-approximation of the social welfare (where n is an upper bound on the maximum integral coordinate of each rectangle). We also consider the non-single-minded case, and design a randomized truthful-in-expectation mechanism with approximation guarantee O(1) (respectively, O(logm)).