Random assignments on preference domains with a tier structure

Abstract

We address a standard random assignment problem (Bogomolnaia and Moulin, 2001). A weakly connected domain admitting an sd-strategy-proof, sd-efficient and equal-treatment-of-equals rule is characterized to be a restricted tier domain. Conversely, on such a domain, the probabilistic serial rule is uniquely characterized by either sd-strategy-proofness, sd-efficiency and equal treatment of equals, or sd-efficiency and sd-envy-freeness. Moreover, we provide an algorithm to construct unions of multiple restricted tier domains, each of which admits an sd-strategy-proof, sd-efficient and sd-envy-free rule.