Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems

We consider the problem of allocating indivisible objects when agents may desire to consume more than one object and monetary transfers are not possible. Each agent receives a set of objects and free disposal is allowed. We are interested in allocation rules that satisfy appealing properties from an economic and social point of view. Our main result shows that sequential dictatorships are the only efficient and coalitional strategy-proof solutions to the multiple assignment problem. Adding resource-monotonicity narrows this class down to serial dictatorships.We thank Francois Maniquet, two anonymous referees, and the participants of the GREBE-FRANCQUI Summer School on Axiomatic Resource Allocation Theory, held in Namur, Belgium, for their comments.