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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随机需求下独占许可市场频谱租赁的最优期限


本文解决了以下问题，该问题对于设计通过频谱拍卖出售的高效专用频谱许可证很有意义。给定一个系统模型，其中客户需求、收入和无线运营商的出价具有随机过程的特点，并且只有当运营商的预期收入高于阈值且租赁期限低于阈值时，运营商才有兴趣加入市场，那么最大化无线运营商服务的净客户需求的最佳租赁期限？增加或减少租赁期限会产生许多相互竞争的影响；较短的租赁期限可能会提高频谱分配的效率，而较长的租赁期限可能会激励更多运营商进入市场，从而增加市场竞争。我们将此问题表述为由调节器和无线运营商组成的两阶段 Stackelberg 博弈，并设计有效的算法来找到整个博弈的 Stackelberg 均衡。这些算法还可用于在我们模型的某些推广下找到 Stackelberg 平衡。使用这些算法，我们获得了重要的数值结果和见解，描述了最佳租赁期限如何随市场参数变化，以最大限度地提高频谱利用率。我们的一些数值结果并不直观，因为它们表明增加市场竞争不一定会提高频谱利用率。据我们所知，本文提出了第一个优化频谱许可证租赁期限的数学方法。