Near-Optimal Truthful Auction Mechanisms in Secondary Spectrum Markets

TL;DR

This paper develops near-optimal truthful auction mechanisms for secondary spectrum markets, addressing the NP-hard spectrum allocation problem by leveraging LP-based techniques and proving their approximation guarantees.

Contribution

It introduces bid-monotone, near-optimal spectrum allocation mechanisms with provable approximation bounds for social efficiency and revenue.

Findings

Mechanisms achieve at least (1 - 1/e) approximation of optimal social efficiency.

Mechanisms are proven to be truthful via bid monotonicity.

Simulation results validate theoretical performance guarantees.

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.