Truthful Auction Analysis and Design in Multiunit Heterogenous Spectrum Markets With Reserve Prices

Abstract

We a practical multiunit heterogeneous spectrum market in which each buyer may request multiple channels with different bid prices at different geographical regions and each channel is associated with a reserve price indicating the desired revenue of the seller. The degree-of-freedom brought by multiunit trading and (reserve and bid) price diversity in such a market can be exploited to break the truthfulness of the two most popular schemes adopted by secondary spectrum auctions, namely Myerson's Optimal Mechanism (MOM) and Vickrey-Clarke-Groves (VCG), via bidder self-collusion. In this paper, we conduct a thorough analysis on the root causes of untruthfulness in MOM and VCG, and prove the fundamental theories addressing when MOM and VCG are truthful and when their truthfulness is broken by bid rigging. Particularly, we demonstrate how self-collusion is exploited in MOM and VCG to improve the untruthful bidders' utility. The critical findings provide a guidance for us to design a Self-collusion Resistant Auction (SIRI) in multiunit heterogeneous spectrum markets with reserve prices. The economic properties of SIRI are proved via rigorous theoretical analysis.