With the increasing demands for radio spectrum, techniques are being explored that would allow dynamic access of spectrum bands that are underutilized. In this regard, a new paradigm called dynamic spectrum access is being investigated where wireless service providers (WSPs) would dynamically seek more spectrum from the under-utilized licensed bands when and where they need without interfering with the primary users. Currently, there is little understanding on how such a dynamic allocation will operate so as to make the system feasible under economic terms. In this paper, we consider the dynamic spectrum allocation process where multiple WSPs (bidders) compete to acquire necessary spectrum band from a common pool of spectrum. We use auction theory to analyze the allocation process when the demand from WSPs exceeds the available spectrum. We investigate various auction mechanisms under different spectrum allocation constraints to find WSPs’ bidding strategies and revenue generated by spectrum owner. We show that sequential bidding of bands provides better result than the concurrent bidding when WSPs are constrained to at most single unit allocation. On the other hand, when the bidders request for multiple units, (i.e., they are S. Sengupta · M. Chatterjee (B) School of Electrical Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA e-mail: firstname.lastname@example.org S. Sengupta e-mail: email@example.com not restricted by allocation constraints) synchronous auction mechanism proves to be beneficial than asynchronous auctions.