  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.
