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.

中文翻译：

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具有保留价格的多单元异构频谱市场的真实拍卖分析和设计

我们建立了一个实用的多单元异构频谱市场，其中每个买方可以在不同的地理区域请求具有不同出价的多个渠道，并且每个渠道都与表示卖方期望收入的底价相关联。可以利用这种市场中多单位交易和（保留和出价）价格多样性带来的自由度来打破二级频谱拍卖采用的两种最受欢迎​​的方案的真实性，即Myerson的最优机制（MOM）和Vickrey -克拉克-格罗夫（Clarke-Groves）（VCG），通过竞标者的自我勾结。在本文中，我们对MOM和VCG中不真实的根本原因进行了透彻的分析，并证明了当MOM和VCG为真实时以及通过操纵投标破坏其真实性时所针对的基本理论。特别，我们演示了如何在MOM和VCG中利用自我共谋来提高虚假竞标者的效用。关键的发现为我们在具有底价的多单元异构频谱市场中设计抗自拍拍卖（SIRI）提供了指导。通过严格的理论分析证明了SIRI的经济性质。