For decades, Simultaneous Ascending Auction (SAA) has been the most popular mechanism used for spectrum auctions. It has recently been employed by many countries for the allocation of 5G licences. Although SAA presents relatively simple rules, it induces a complex strategic game for which the optimal bidding strategy is unknown. Considering the fact that sometimes billions of euros are at stake in an SAA, establishing an efficient bidding strategy is crucial. In this work, we model the auction as a $n$-player simultaneous move game with complete information and propose the first efficient bidding algorithm that tackles simultaneously its four main strategic issues: the $\textit{exposure problem}$, the $\textit{own price effect}$, $\textit{budget constraints}$ and the $\textit{eligibility management problem}$. Our solution, called $SMS^\alpha$, is based on Simultaneous Move Monte Carlo Tree Search (SM-MCTS) and relies on a new method for the prediction of closing prices. By introducing a new reward function in $SMS^\alpha$, we give the possibility to bidders to define their own level of risk-aversion. Through extensive numerical experiments on instances of realistic size, we show that $SMS^\alpha$ largely outperforms state-of-the-art algorithms, notably by achieving higher expected utility while taking less risks.

翻译：数十年来，同步升价拍卖(SAA)一直是频谱拍卖领域最主流的机制。近年来，许多国家采用该机制分配5G牌照。尽管SAA规则相对简单，但其引发的复杂策略博弈中最优竞价策略仍属未知。考虑到单次SAA常涉及数十亿欧元资金，建立高效竞价策略至关重要。本研究将拍卖建模为具有完全信息的$n$人同时行动博弈，首次提出能同时应对四大核心策略问题的竞价算法：$\textit{暴露问题}$、$\textit{自身价格效应}$、$\textit{预算约束}$与$\textit{资格管理问题}$。本方案命名为$SMS^\alpha$，基于同时行动蒙特卡洛树搜索(SM-MCTS)技术，并依托闭合价格预测新方法。通过在$SMS^\alpha$中引入新型奖励函数，投标者得以自主设定风险厌恶水平。基于实际规模实例的大规模数值实验表明，$SMS^\alpha$显著优于现有最优算法，尤其在实现更高期望效用的同时承担更低风险方面表现突出。