Simple Clock Auctions (SCA) are a mechanism commonly used in spectrum auctions to sell lots of frequency bandwidths. We study such an auction with one player having access to perfect information against straightforward bidders. When the opponents' valuations satisfy the ordinary substitutes condition, we show that it is optimal to bid on a fixed lot overtime. In this setting, we consider a continuous-time version of the SCA auction in which the prices follow a differential inclusion with a piecewise-constant dynamics. We show that there exists a unique solution in the sense of Filippov. This guarantees that the continuous-time model coincides with the limit of the discrete-time auction when price increments tend to zero. Moreover, we show that the value function of this limit auction is piecewise linear (though possibly discontinuous). Finally, we illustrate these results by analyzing a simplified version of the multiband Australian spectrum auction of 2017.

翻译：简单时钟拍卖（SCA）是频谱拍卖中常用于出售频段资源的机制。本文研究一种拍卖场景，其中一名参与者拥有完全信息，而其他竞标者采用直接竞价策略。当对手的估值满足普通替代品条件时，我们证明在固定频段上持续出价是最优策略。在此框架下，我们构建了SCA拍卖的连续时间版本，其价格遵循具有分段常数动态的微分包含关系。我们证明该模型在Filippov意义下存在唯一解，这确保了当价格增量趋近于零时，连续时间模型与离散时间拍卖的极限行为一致。此外，我们证明该极限拍卖的价值函数具有分段线性特征（可能存在间断点）。最后，我们通过分析2017年澳大利亚多频段频谱拍卖的简化模型来验证上述结论。