Group stability in matching with interdependent values

We study two-sided many-to-one matching markets with interdependent valuations and imperfect information held by one side of the market. The other side has common and known preferences over potential mates. In this setting, pairwise stability does not imply group stability: mechanisms that are stable with respect to deviations by pairs of agents may be vulnerable to deviations by groups. We formalize a notion of group stability and construct a “modified serial dictatorship” mechanism that implements group stable matchings. We further discuss the robustness of our notion of stability and examine efficiency properties of modified serial dictatorship.