The York Research Database

This paper studies an allocation problem with multiple object assignments, indivisible objects, no endowments and no monetary transfers. Agents have complete, transitive and strict preferences over bundles of objects. A rule assigns objects to agents. A single object may be assigned to several agents as long as the agents satisfy a compatibility constraint. If no restrictions are imposed on the compatibility structure, there exists no rule that satisfies Pareto efficiency and compatibility-monotonicity. Imposing two restrictions on the compatibility structure, the class of rules called compatibility-sorting sequential dictatorships can be fully characterized by four different combinations of group-strategyproofness, strategyproofness, Pareto efficiency, non-bossiness, compatibility-monotonicity and compatibility-invariance. It is demonstrated that the characterization in Pápai (J Public Econ Theory 3:258–271, 2001) of sequential dictatorships for the case where assignments are not allowed to overlap is contained as a special case of the main result. Finally, some additional properties are considered and an extension of the model introducing capacity constraints is presented.