| Abstract: |
We study the random assignments of bundles with no free disposal. The key
difference between the setting with bundles and the setting with objects (see
Bogomolnaia and Moulin (2001)) is one of feasibility. The implications of this
difference are significant. First, the characterization of sd-efficient random
assignments is fundamentally different. Second, a possibility result in the
setting with objects fails in the setting with bundles. However, in the
setting with bundles, 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 sdefficiency,
sd-strategy-proofness, and equal treatment of equals. Moreover, this rule
selects only random assignments which can be decomposed as convex combinations
of deterministic assignments. |