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原文摘要

The game "Mafia'' is a social deduction game where $n$ players attempt to uncover a covert coalition of $m$ players among the $n$. Typically, $d=1$ of the non-coalition players are labelled ``Detective'' and have special abilities. Most game-theoretic analysis considers, however, only the variant without a Detective. Once the Detective role is introduced, extremely complex strategies can be employed, for which reason only upper and lower bounds for winning have been established, namely by considering specific strategies. We analyse the case $m=d=1$, providing a first example where an explicit, provably-optimal strategy can be described beyond $d=0$.