Constrained Efficiency and Strategy-Proofness in Package Assignment Problems with Money

We consider a package assignment problem with money, in which a finite set M of objects is allocated to agents. Each agent receives a package of objects and makes a payment, and has preferences over pairs consisting of a package and a payment. These preferences are not necessarily quasi-linear. The admissible set of object allocations is chosen by the planner to pursue specific objectives in conjunction with the rule. A rule satisfies constrained efficiency if no allocation―whose object allocation is admissible under the rule―Pareto dominates the allocation selected by the rule. We study the compatibility between constraints on admissible object allocations and desirable properties of rules, and characterize the rules that satisfy both. We establish that: A rule satisfies constrained efficiency, no wastage, equal treatment of equals, strategy-proofness, individual rationality, and no subsidy if and only if its admissible set of object allocations is bundling unit-demand for some partition of M, satisfies no wastage and anonymity, and the rule is a bundling unit-demand minimum price Walrasian rule.