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 strategical game for which the optimal bidding strategy is unknown. Considering the fact that sometimes billions of euros are at stake in a 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 strategical 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 scalarised rewards 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：几十年来，同步加价拍卖（SAA）一直是频谱拍卖中最常用的机制。近年来，许多国家将其用于5G牌照的分配。尽管SAA的规则相对简单，但其引发的策略博弈极为复杂，而最优投标策略至今未知。考虑到SAA中常涉及数十亿欧元的标的，制定高效投标策略至关重要。本文将拍卖建模为具有完全信息的n人同时移动博弈，并首次提出能同时应对四大核心策略问题的高效投标算法：暴露问题、自身价格效应、预算约束与资格管理问题。该算法命名为SMS^α，基于同时移动蒙特卡洛树搜索（SM-MCTS），并采用新的收盘价预测方法。通过在SMS^α中引入标量化奖励，我们允许竞标者自定义风险规避水平。基于真实规模实例的广泛数值实验表明，SMS^α在显著提升期望效用的同时降低了风险，整体性能大幅优于现有最优算法。