Optimal Auctions in Oligopoly Spectrum Market with Concealed Cost

This paper presents a mathematical approach to the future dynamic spectrum market, where multiple secondary operators compete to gain radio resources. The secondary network operators (SNOs) face various concurrent auctions. We discuss techniques, which can be used to select auctions to optimize their objectives and increase the winning probability. To achieve these goals, a matching problem is formulated and solved, where secondary operators are paired with auctions, which can provide spectrum with the highest expected quality of service (QoS). A total outlay optimization is structured for auctions with concealed reserve prices, which are only revealed to the secondary operators for some price upon request. More specifically, we solve a nonlinear problem to determine the minimum set of auctions by using the brute force algorithm. We further introduce a surplus maximization and demonstrate an auction mechanism of spectrum allocation by modifying the Bayesian-Nash equilibrium. The mathematical analyses highlight that the optimal choice is achievable through the proposed mathematical formulation.