  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.
