Random Assignment Respecting Group Priorities∗

When allocating indivisible objects, agents may be partitioned into several groups and different groups are granted different priority rights. Group-wise random serial dictatorship (GRSD) and group-wise probabilistic serial mechanism (GPS) can be applied to such problems to restore fairness within and across groups. GPS outperforms GRSD not only in efficiency but also in stability ex-ante. The family of group-wise eating mechanisms characterizes the set of sd-efficient and ex-ante stable assignments, while the family of asymmetric GRSDs characterizes the set of ex-post stable and efficient assignments. However, GRSD satisfies a mild consistency concept based on Bayesian update while GPS does not, and consequently the advantages of GPS may disappear in cases of non-simultaneous assignment. We finish by characterizing GPS and considering comparative statics results as the group structure becomes more dense.