Random assignment of bundles

• Main Authors: CHATTERJI, Shurojit, LIU, Peng
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Random assignments; bundles; decomposability; sd-efficiency; sd-strategy-proofness; equal treatment of equals; Economics; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2201; https://ink.library.smu.edu.sg/context/soe_research/article/3200/viewcontent/RandomAssignmentsOfBundles___1_.pdf
• Institution: Singapore Management University

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 sd-efficiency, 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.