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.

中文翻译：

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具有随机需求的专有许可市场中频谱租赁的最优期限

本文解决了以下问题，这对设计通过频谱拍卖出售的有效专用频谱许可证很有用。给定一个系统模型，其中无线运营商的客户需求，收入和出价以随机过程为特征，并且只有当其预期收入超过阈值且租赁期限低于阈值时，运营商才有兴趣加入市场，这是什么？最佳租用期限能最大化无线运营商服务的净客户需求？增加或减少租赁期限会产生许多竞争影响。较短的租赁期限可以提高频谱分配的效率，而较长的租赁期限可以通过激励更多运营商进入市场来增强市场竞争。我们将此问题公式化为由调节器和无线运营商组成的两阶段Stackelberg游戏，并设计有效的算法以找到整个游戏的Stackelberg平衡。在我们模型的某些概括下，这些算法也可用于找到Stackelberg平衡。使用这些算法，我们获得了重要的数值结果和见解，这些见解描述了最佳租赁期限如何相对于市场参数而变化，从而最大限度地利用了频谱。我们的一些数值结果是不直观的，因为它们表明日益激烈的市场竞争未必会提高频谱利用率。据我们所知，本文提出了第一种数学方法来优化频谱许可证的租赁期限。