For decades, Simultaneous Ascending Auction (SAA) has been the most widely used mechanism for spectrum auctions, and it has recently gained popularity for allocating 5G licenses in many countries. Despite its relatively simple rules, SAA introduces a complex strategic game with an unknown optimal bidding strategy. Given the high stakes involved, with billions of euros sometimes on the line, developing an efficient bidding strategy is of utmost importance. In this work, we extend our previous method, a Simultaneous Move Monte-Carlo Tree Search (SM-MCTS) based algorithm named $SMS^{\alpha}$ to incomplete information framework. For this purpose, we compare three determinization approaches which allow us to rely on complete information SM-MCTS. This algorithm addresses, in incomplete framework, the four key strategic issues of SAA: the exposure problem, the own price effect, budget constraints, and the eligibility management problem. Through extensive numerical experiments on instances of realistic size with an uncertain framework, we show that $SMS^{\alpha}$ largely outperforms state-of-the-art algorithms by achieving higher expected utility while taking less risks, no matter which determinization method is chosen.

翻译：数十年来，同步增价拍卖（SAA）一直是频谱拍卖中应用最广泛的机制，近年来更在许多国家的5G许可证分配中日益普及。尽管其规则相对简单，SAA却构成了一个策略复杂的博弈，其最优竞价策略尚不明确。考虑到其中涉及的高额利益——有时高达数十亿欧元——开发高效的竞价策略至关重要。在本研究中，我们将先前提出的基于同步移动蒙特卡洛树搜索（SM-MCTS）的算法$SMS^{\alpha}$扩展至不完全信息框架。为此，我们比较了三种确定性转换方法，使我们能够依赖完全信息下的SM-MCTS。该算法在不完全信息框架下解决了SAA的四个关键策略问题：风险暴露问题、自身价格效应、预算约束以及资格管理问题。通过在不确定框架下对现实规模算例进行大量数值实验，我们证明无论选择何种确定性转换方法，$SMS^{\alpha}$算法均显著优于现有最优算法，在承担更低风险的同时实现了更高的期望效用。