  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.
