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 nk and is characteristic to each model.Comment: SAGT 202