Near-Optimal Truthful Auction Mechanisms in Secondary Spectrum Markets

Abstract: In this work, we study spectrum auction problem where each request from secondary users has spatial, temporal, and spectral features. With the requests of secondary users and the reserve price of the primary user, our goal is to design truthful mechanisms that will either maximize the social efficiency or maximize the revenue of the primary user. As the optimal conflict-free spectrum allocation problem is NP-hard, in this work, we design near optimal spectrum allocation mechanisms separately based on the following techniques: derandomized allocation from integer programming formulation, its linear programming (LP) relaxation, and the dual of the LP. We theoretically prove that 1) our near optimal allocation methods are bid monotone, which implys truthful auction mechanisms; and 2) our near optimal allocation methods can achieve a social efficiency or a revenue that is at least $1-\frac{1}{e}$ times of the optimal respectively. At last, we conduct extensive simulations to study the performances (social efficiency, revenue) of the proposed methods, and the simulation results corroborate our theoretical analysis.