论文标题
Galton-Watson树上的组合游戏，涉及多个生成动作
Combinatorial games on Galton-Watson trees involving several-generation-jump moves
论文作者
论文摘要
我们研究了$ k $ - 跳跃的正常和$ k $ - $ - $ -SH的MISère游戏，上面扎根的Galton-Watson树上，表达了这些游戏的各种结果的概率，这是依赖$ K $和后代分布的某些功能的特定固定点。我们讨论了有关在后代分布是泊松$（λ）$（即，对于$λ$的值，绘制概率严格为正的值）时，讨论了与提取概率有关的相关结果。我们将$ 2 $ - 跳跃的普通游戏的各种结果的概率与$ 2 $ - 跳跃的Misère游戏的概率进行了比较，在Poisson Imime下，在$ 2 $ - 跳跃的普通游戏和$ 1 $ - 跳跃的普通游戏之间也有类似的比较。我们将第一位玩家损失$ 2 $ - 跳跃普通游戏的衰减率描述为$λ\ rightarrow \ infty $。最后，我们讨论了$ k $跳跃的普通游戏的平均持续时间有限的足够持续时间。
We study the $k$-jump normal and $k$-jump misère games on rooted Galton-Watson trees, expressing the probabilities of various outcomes of these games as specific fixed points of certain functions that depend on $k$ and the offspring distribution. We discuss results on phase transitions pertaining to draw probabilities when the offspring distribution is Poisson$(λ)$ (i.e. for which values of $λ$, the draw probability is strictly positive). We compare the probabilities of the various outcomes of the $2$-jump normal game with those of the $2$-jump misère game, and a similar comparison is drawn between the $2$-jump normal game and the $1$-jump normal game, under the Poisson regime. We describe the rate of decay of the probability that the first player loses the $2$-jump normal game as $λ\rightarrow \infty$. Finally, we discuss a sufficient condition for the average duration of the $k$-jump normal game to be finite.
