Strategyproof and Nonbossy Multiple Assignments

We consider the allocation of heterogeneous indivisible objects without using monetary transfers. Each agent may be assigned more than one object. We show that an allocation rule is strategyproof, nonbossy, and satisfies citizen sovereignty if and only if it is a sequential dictatorship. In a sequential dictatorship agents are assigned their favorite objects that are still available, according to a sequentially endogenously determined hierarchy of the agents. We also establish that replacing nonbossiness by a stronger criterion restricts the characterized class of allocation rules to serial dictatorships, in which the hierarchy of the agents is fixed a priori.