We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more beneficial to at least $k$ out of the $n$ agents. The concept generalizes the recently studied majority stability. We prove that whereas the verification of $k$-stability for a given matching is polynomial-time solvable in all three models, the complexity of deciding whether a $k$-stable matching exists depends on $\frac{k}{n}$ and is characteristic to each model.

翻译：我们研究了三类主要匹配市场（房屋分配、婚姻和室友模型）中代理群体的偏离行为。对于给定实例，若不存在另一个匹配使得至少$k$个（共$n$个）代理受益更多，则称该匹配为$k$-稳定的。该概念推广了近期研究的多数稳定性。我们证明，虽然验证给定匹配的$k$-稳定性在三个模型中均可多项式时间求解，但判定是否存在$k$-稳定匹配的复杂度取决于$\frac{k}{n}$，且各模型具有不同特征。