Truthful mechanisms for exhibitions

Authors:
George Christodoulou;Khaled Elbassioni;Mahmoud Fouz
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany and Cluster of Excellence "Multimodal Computing and Interaction", Universität des, Saarlandes;Max-Planck-Institut für Informatik, Saarbrücken, Germany;FR Informatik, Universität des Saarlandes, Saarbrücken, Germany
Venue:
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Year:
2010

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Abstract

We consider the following combinatorial auction: Given a range space (U,R), and m bidders interested in buying only ranges in R, each bidder j declares her bid bj :R → R+. We give a deterministic truthful mechanism, when the valuations are single-minded: when R is a collection of fat objects (respectively, axis-aligned rectangles) in the plane, there is a truthful mechanism with a 1 + ε- (respectively, ⌈log n⌉)- 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-inexpectation mechanism with approximation guarantee O(1) (respectively, O(log m)).