Spot Pricing of Wireless Spectrum in Secondary Markets - 09/12/2008

Huseyin Mutlu

Recent deregulation initiatives enable cellular providers to sell excess spectrum for secondary usage. In this Ph.D. prospectus proposal, we investigate the problem of efficient real-time pricing of spectrum in the presence of both non-elastic primary users, with long-term commitments, and opportunistic, elastic secondary users.

We show that optimal pricing by a provider can be formulated as an infinite horizon average reward problem and solved using stochastic dynamic programming. We investigate the design of efficient single pricing policies and provide evidences that static pricing policies do not perform well in such settings (in sharp contrast to settings where all the users are elastic). On the other hand, we prove that deterministic threshold pricing achieves optimal profit amongst all single-price policies and performs close to global optimal pricing. We characterize the profit regions of different pricing policies, as a function of the arrival rate of primary users. Under certain reasonable assumptions on the demand function, we prove that the profit region of threshold pricing is: 1) optimal and independent of the specific form of the demand function; 2) larger than that of static pricing; and 3) unimodal in price. Furthermore, we show that the optimal threshold policy can be computed far faster than the global optimal policy.

We also propose future directions for our research. One goal is to devise adaptive pricing methods that can adjust to changing system statistics. We propose preliminary versions of such adaptive algorithms for dynamic and threshold pricing algorithms. Another goal is to characterize pricing strategies and equilibria in a duopoly market, i.e., in the presence of a competing spectrum provider.