Cooperative 2-matching games are a generalization of cooperative matching games, where the value function is given by maximum-weight b-matchings, for a vertex capacity vector $b \leq 2$. We show how to separate over the core of 2-matching games in polynomial time, fixing a small flaw in the literature, and prove the existence of a compact extended formulation for it.

翻译：合作2-匹配博弈是合作匹配博弈的推广，其中价值函数由最大权b-匹配给出，顶点容量向量满足$b \leq 2$。我们展示了如何在多项式时间内对2-匹配博弈的核心进行分离，修正了文献中的一个小缺陷，并证明了其紧致扩展形式的存在性。