Constrained efficiency and strategy-proofness in package assignment problems with money

We consider a package assignment problem with money, in which a set M of objects is allocated to agents. Each agent has preferences that 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 outcome allocation. We study the compatibility between constraints on admissible object allocations and desirable properties of rules, and establish: A rule satisfies constrained efficiency and strategy-proofness, together with other mild properties, if and only if its admissible set 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.