We study the applicability of quantum algorithms in computational game theory and generalize some results related to Subtraction games, which are sometimes referred to as one-heap Nim games. In quantum game theory, a subset of Subtraction games became the first explicitly defined class of zero-sum combinatorial games with provable separation between quantum and classical complexity of solving them. For a narrower subset of Subtraction games, an exact quantum sublinear algorithm is known that surpasses all deterministic algorithms for finding solutions with probability $1$. Typically, both Nim and Subtraction games are defined for only two players. We extend some known results to games for three or more players, while maintaining the same classical and quantum complexities: $\Theta\left(n^2\right)$ and $\tilde{O}\left(n^{1.5}\right)$ respectively.

中文翻译：

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解决多人游戏的量子超越经典优势

我们研究了量子算法在计算博弈论中的适用性，并概括了一些与减法博弈相关的结果，这些博弈有时被称为单堆 Nim 博弈。在量子博弈论中，减法博弈的一个子集成为第一个明确定义的零和组合博弈类，在解决它们的量子复杂性和经典复杂性之间可证明分离。对于较窄的减法游戏子集，已知一种精确的量子次线性算法，它超越了所有确定性算法，可以找到概率为 $1$ 的解。通常，Nim 和 Subtraction 游戏都是为两个玩家定义的。我们将一些已知结果扩展到三个或更多玩家的游戏，同时保持相同的经典和量子复杂度：$\Theta\left(n^2\right)$ 和 $\tilde{O}\left(n^{1.5} \right)$ 分别。