On the Optimal Duration of Spectrum Leases in Exclusive License Markets with Stochastic Demand

Abstract: This paper addresses the following question which is of interest in designing efficient exclusive-use spectrum licenses sold through spectrum auctions. Given a system model in which customer demand, revenue, and bids of wireless operators are characterized by stochastic processes and an operator is interested in joining the market only if its expected revenue is above a threshold and the lease duration is below a threshold, what is the optimal lease duration which maximizes the net customer demand served by the wireless operators? Increasing or decreasing lease duration has many competing effects; while shorter lease duration may increase the efficiency of spectrum allocation, longer lease duration may increase market competition by incentivizing more operators to enter the market. We formulate this problem as a two-stage Stackelberg game consisting of the regulator and the wireless operators and design efficient algorithms to find the Stackelberg equilibrium of the entire game. These algorithms can also be used to find the Stackelberg equilibrium under some generalizations of our model. Using these algorithms, we obtain important numerical results and insights that characterize how the optimal lease duration varies with respect to market parameters in order to maximize the spectrum utilization. A few of our numerical results are non-intuitive as they suggest that increasing market competition may not necessarily improve spectrum utilization. To the best of our knowledge, this paper presents the first mathematical approach to optimize the lease duration of spectrum licenses.