Random assignments of bundles

Abstract

We propose a model studying the random assignments of bundles with no free disposal. The key difference between our model and the one where objects are allocated (see Bogomolnaia and Moulin (2001)) is one of feasibility. The implications of this difference are significant. Firstly, the characterization of sd-efficient random assignments is more complex. Secondly, we are able to identify a preference restriction, called essential monotonicity, under which the random serial dictatorship rule (extended to the setting with bundles) is equivalent to the probabilistic serial rule (extended to the setting with bundles). This equivalence implies the existence of a rule on this restricted domain satisfying sd-efficiency, sd-strategy-proofness, and equal treatment of equals. Moreover, this rule only selects random assignments which can be decomposed as convex combinations of deterministic assignments.