Core-Selecting Secondary Spectrum Auctions

In a secondary spectrum market, the utility of a secondary user often depends on not only whether it wins, but also which channels it wins. Combinatorial auctions are a natural fit here to allow secondary users to bid for combinations of channels. In this context, the VCG mechanism constitutes a generic auction that uniquely guarantees both truthfulness and efficiency. There also exists related auction design that relaxes efficiency due to perceived complexity issues, and focuses on truthfulness. Starting with new empirical evidences on the complexity issue, we propose to design core-selecting auctions instead, which resolve VCG's vulnerability to collusion and shill bidding, and improve seller revenue. While the VCG type of auctions are unique in guaranteeing both efficiency and truthfulness, we prove that our core-selecting auctions are unique in guaranteeing both efficiency and shill-proofness, and always outperform VCG auctions in terms of seller revenue generated. Employing linear programming and quadratic programming techniques, we design two payment rules for minimizing the incentives of bidders to deviate from truth telling.