If $G$ is a bipartite graph, Hall's theorem \cite{H35} gives a condition for the existence of a matching of $G$ covering one side of the bipartition. This theorem admits a well-known algorithmic proof involving the repeated search of augmenting paths. We present here an alternative algorithm, using a game-theoretic formulation of the problem. We also show how to extend this formulation to the setting of balanced hypergraphs.

翻译：设 $G$ 为二分图，Hall 定理 \cite{H35} 给出了 $G$ 存在覆盖二分图一侧的匹配的条件。该定理有一个众所周知的算法证明，涉及反复搜索增广路径。本文提出一种替代算法，采用问题的博弈论形式。我们还展示了如何将该形式推广到平衡超图的情形。