The theory of $p$-modulus provides a general framework for quantifying the richness of a family of objects on a graph. When applied to the family of spanning trees, $p$-modulus has an interesting probabilistic interpretation. In particular, the $2$-modulus problem in this case has been shown to be equivalent to the problem of finding a probability distribution on spanning trees that utilizes the edges of the graph as evenly as possible. In the present work, we use this fact to produce a game-theoretic interpretation of modulus by employing modulus to solve a secure broadcast game.

中文翻译：

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用于安全广播游戏的生成树模数

$p$-modulus 理论为量化图上对象族的丰富度提供了一个通用框架。当应用于生成树族时，$p$-modulus 有一个有趣的概率解释。特别是，在这种情况下，$2$-模问题已被证明等效于在尽可能均匀地利用图的边缘的生成树上找到概率分布的问题。在目前的工作中，我们利用这一事实通过使用模数来解决安全广播博弈来产生模数的博弈论解释。