Based on duality theory of linear programming and graph theory, it is proved that the matching game defined on a bipartite graph has the stable core if and only if the graph has a perfect matching.

• 基于线性规划对偶理论和图论的相关知识，我们首先证明了匹配对策有稳定核心当且仅当其基础二部图有完美匹配。