Group Stability in Matching With Interdependent Values

We study two-sided many-to-one matching markets with interdependent valuations and im-perfect 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 stabil-ity: 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