Reserve Price Auctions for Heterogeneous Spectrum Sharing

Spectrum auction is considered a suitable approach to efficiently allocate spectrum among unlicensed users. In a typical spectrum auction, Secondary Users (SUs) bid to buy spectrum bands from a Primary Owner (PO) who acts as the auctioneer. In this paper, unlike most existing auction mechanisms, spectrum auctions are studied in a realistic setting where channels have different qualities, and SUs are allowed to express their preferences for each channel separately. That is, each SU submits a vector of bids, one for each channel. An efficient spectrum auction is proposed that maximizes the social welfare of the SUs. In addition, a reserve price auction is proposed whereby the PO imposes reserve prices on channels. The paper studies what the optimal reserve prices should be in order to maximize the PO’s revenue. Optimal reserve prices are found provided that the distribution of SUs’ valuations is known. In the case where no prior information is available about valuation distributions, prior-free reserve prices are presented that guarantee at least half of the optimal revenue. The proposed auctions run in polynomial time and have desired economic properties that are formally proven in the analysis. Furthermore, the proposed numerical results show the effect of spectrum heterogeneity and reserve prices on the performance of spectrum auctions.