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This paper addresses the following question which is of interest in designingefficient exclusive-use spectrum licenses sold through spectrum auctions. Givena system model in which customer demand, revenue, and bids of wirelessoperators are characterized by stochastic processes and an operator isinterested in joining the market only if its expected revenue is above athreshold and the lease duration is below a threshold, what is the optimallease duration which maximizes the net customer demand served by the wirelessoperators? Increasing or decreasing lease duration has many competing effects;while shorter lease duration may increase the efficiency of spectrumallocation, longer lease duration may increase market competition byincentivizing more operators to enter the market. We formulate this problem asa two-stage Stackelberg game consisting of the regulator and the wirelessoperators and design efficient algorithms to find the Stackelberg equilibriumof the entire game. These algorithms can also be used to find the Stackelbergequilibrium under some generalizations of our model. Using these algorithms, weobtain important numerical results and insights that characterize how theoptimal lease duration varies with respect to market parameters in order tomaximize the spectrum utilization. A few of our numerical results arenon-intuitive as they suggest that increasing market competition may notnecessarily improve spectrum utilization. To the best of our knowledge, thispaper presents the first mathematical approach to optimize the lease durationof spectrum licenses.

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