Chapter

Internet and Network Economics

Volume 6484 of the series Lecture Notes in Computer Science pp 170-181

Truthful Mechanisms for Exhibitions

  • George ChristodoulouAffiliated withMax-Planck-Institut für InformatikCluster of Excellence “Multimodal Computing and Interaction”, Universität des Saarlandes
  • , Khaled ElbassioniAffiliated withMax-Planck-Institut für Informatik
  • , Mahmoud FouzAffiliated withFR Informatik, Universität des Saarlandes

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Abstract

We consider the following combinatorial auction: Given a range space https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-17572-5_14/MediaObjects/978-3-642-17572-5_14_IEq1_HTML.png , and m bidders interested in buying only ranges in https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-17572-5_14/MediaObjects/978-3-642-17572-5_14_IEq2_HTML.png , each bidder j declares her bid https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-17572-5_14/MediaObjects/978-3-642-17572-5_14_IEq3_HTML.png . We give a deterministic truthful mechanism, when the valuations are single-minded: when https://static-content.springer.com/image/chp%3A10.1007%2F978-3-642-17572-5_14/MediaObjects/978-3-642-17572-5_14_IEq4_HTML.png 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)).